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Sample records for canonical partition function

  1. Subsets of configurations and canonical partition functions

    DEFF Research Database (Denmark)

    Bloch, J.; Bruckmann, F.; Kieburg, M.;

    2013-01-01

    We explain the physical nature of the subset solution to the sign problem in chiral random matrix theory: the subset sum over configurations is shown to project out the canonical determinant with zero quark charge from a given configuration. As the grand canonical chiral random matrix partition f...... function is independent of the chemical potential, the zero-quark-charge sector provides the full result. © 2013 American Physical Society....

  2. A Graphical representation of the grand canonical partition function

    CERN Document Server

    Smii, Boubaker

    2010-01-01

    In this paper we consider a stochastic partial differential equation defined on a Lattice $L_\\delta$ with coefficients of non-linearity with degree $p$. An analytic solution in the sense of formal power series is given. The obtained series can be re-expressed in terms of rooted trees with two types of leaves. Under the use of the so-called Cole-Hopf transformation and for the particular case $p=2$, one thus get the generalized Burger equation. A graphical representation of the solution and its logarithm is done in this paper. A discussion of the summability of the previous formal solutions is done in this paper using Borel sum. A graphical calculus of the correlation function is given. The special case when the noise is of L\\'evy type gives a simplified representations of the solution of the generalized Burger equation. From the previous results we recall a graphical representation of the grand canonical partition function.

  3. Algebraic method for exact solution of canonical partition function in nuclear multifragmentation

    CERN Document Server

    Parvan, A S

    2002-01-01

    An algebraic method for the exact recursion formula for the calculation of canonical partition function of non-interaction finite systems of particles obeying Bose-Einstein, Fermi-Dirac, Maxwell-Boltzmann statistics or parastatistics is derived. A new exactly solvable multifragmentation model with baryon and electric charge conservation laws is developed. Recursion relations for this model are presented that allow exact calculation of canonical partition function for any statistics.

  4. A simple way of approximating the canonical partition functions in statistical mechanics

    Science.gov (United States)

    Fernández, Francisco M.

    2015-09-01

    We propose a simple pedagogical way of introducing the Euler-MacLaurin summation formula in an undergraduate course on statistical mechanics. The reason is that the students may feel more comfortable and confident if they are able to deduce the main equations. To this end we put forward two alternative routes: the first one is the simplest and yields the first two terms of the expansion. The second one is somewhat more elaborate and takes into account all the correction terms. We apply both to the calculation of the simplest one-particle canonical partition functions for the translational, vibrational and rotational degrees of freedom. The more elaborate, systematic calculation of the correction terms is suitable for motivating the students to explore the possibility of using available computer algebra software that enable one to avoid long and tedious manipulation of algebraic equations.

  5. Development of particle multiplicity distributions using a general form of the grand canonical partition function

    Science.gov (United States)

    Lee, S. J.; Mekjian, A. Z.

    2004-01-01

    Various phenomenological models of particle multiplicity distributions are discussed using a general form of a unified model which is based on the grand canonical partition function and Feynman's path integral approach to statistical processes. These models can be written as special cases of a more general distribution which has three control parameters which are a, x, z. The relation to these parameters to various physical quantities are discussed. A connection of the parameter a with Fisher's critical exponent τ is developed. Using this grand canonical approach, moments, cumulants and combinants are discussed and a physical interpretation of the combinants are given and their behavior connected to the critical exponent τ. Various physical phenomena such as hierarchical structure, void scaling relations, Koba-Nielson-Olesen or KNO scaling features, clan variables, and branching laws are shown in terms of this general approach. Several of these features which were previously developed in terms of the negative binomial distribution are found to be more general. Both hierarchical structure and void scaling relations depend on the Fisher exponent τ. Applications of our approach to the charged particle multiplicity distribution in jets of L3 and H1 data are given.

  6. Maps of zeros of the grand canonical partition function in a statistical model of high energy collisions

    CERN Document Server

    Brambilla, M; Ugoccioni, R

    2006-01-01

    Theorems on zeros of the truncated generating function in the complex plane are reviewed. When examined in the framework of a statistical model of high energy collisions based on the negative binomial (Pascal) multiplicity distribution, these results lead to maps of zeros of the grand canonical partition function which allow us to interpret in a novel way different classes of events in pp collisions at LHC c.m. energies.

  7. Maps of zeros of the grand canonical partition function in a statistical model of high energy collisions

    Science.gov (United States)

    Brambilla, M.; Giovannini, A.; Ugoccioni, R.

    2006-06-01

    Theorems on zeros of the truncated generating function in the complex plane are reviewed. When examined in the framework of a statistical model of high energy collisions based on the negative binomial (Pascal) multiplicity distribution, these results lead to maps of zeros of the grand canonical partition function which allow us to interpret in a novel way different classes of events in pp collisions at LHC c.m. energies.

  8. Maps of zeroes of the grand canonical partition function in a statistical model of high energy collisions

    OpenAIRE

    Brambilla, M.; Giovannini, A.; Ugoccioni, R.

    2005-01-01

    Theorems on zeroes of the truncated generating function in the complex plane are reviewed. When examined in the framework of a statistical model of high energy collisions based on the negative binomial (Pascal) multiplicity distribution, these results lead to maps of zeroes of the grand canonical partition function which allow to interpret in a novel way different classes of events in pp collisions at LHC c.m. energies.

  9. Comparison of various models of particle multiplicity distributions using a general form of the grand canonical partition function

    CERN Document Server

    Lee, S J

    2002-01-01

    Various phenomenological models of particle multiplicity distributions are discussed using a general form of the grand canonical partition function. These phenomenological models include a wide range of varied processes such as coherent emission or Poisson processes, chaotic emission resulting in a negative binomial distribution, combinations of coherent and chaotic processes called signal/noise distributions, and models based on field emission from Lorentzian line shapes leading to Lorentz/Catalan distributions. These specific cases can be written as special cases of a more general distribution. Using this grand canonical approach moments and cumulants, combinants, hierarchical structure, void scaling relations, KNO scaling features, clan variables and branching laws associated with stochastic or ancestral variables are discussed. It is shown that just looking at the mean and fluctuation of data is not enough to distinguish these distributions or the underlying mechanism. A generalization of the Poisson tran...

  10. Development of particle multiplicity distributions using a general form of the grand canonical partition function and applications to L3 and H1 Data

    OpenAIRE

    Lee, S. J.; Mekjian, A. Z.

    2003-01-01

    Various phenomenological models of particle multiplicity distributions are discussed using a general form of a unified model which is based on the grand canonical partition function and Feynman's path integral approach to statistical processes. These models can be written as special cases of a more general distribution which has three control parameters which are $a$, $x$, $z$. The relation to these parameters to various physical quantities are discussed. A connection of the parameter $a$ wit...

  11. Development of particle multiplicity distributions using a general form of the grand canonical partition function and applications to L3 and H1 Data

    CERN Document Server

    Lee, S J

    2004-01-01

    Various phenomenological models of particle multiplicity distributions are discussed using a general form of a unified model which is based on the grand canonical partition function and Feynman's path integral approach to statistical processes. These models can be written as special cases of a more general distribution which has three control parameters which are $a$, $x$, $z$. The relation to these parameters to various physical quantities are discussed. A connection of the parameter $a$ with Fisher's critical exponent $\\tau$ is developed. Using this grand canonical approach, moments, cumulants and combinants are discussed and a physical interpretation of the combinants are given and their behavior connected to the critical exponent $\\tau$. Various physical phenomena such as hierarchical structure, void scaling relations, KNO scaling features, clan variables, and branching laws are shown in terms of this general approach. Several of these features which were previously developed in terms of the negative bino...

  12. Signatures of the Berezinskii-Kosterlitz-Thouless transition on the zeros of the canonical partition function for the 2D XY-model

    Science.gov (United States)

    Rocha, Julio; Mol, Lucas; Costa, Bismarck

    2015-03-01

    In this work we show that the canonical partition function zeros, the Fisher zeros, can be used to uniquely characterize a transition as being in the Berezinskii-Kosterlitz-Thouless (BKT) class of universality. By studying the zeros map for the 2D XY model we found that its internal border coalesces into the real positive axis in a finite region corresponding to temperatures smaller than the BKT transition temperature. This behavior is consistent with the predicted existence of a line of critical points below the transition temperature, allowing one to distinguish the BKT class of universality from other ones. This work was partially supported by CNPq and Fapemig, Brazilian Agencies.

  13. Functional Multiple-Set Canonical Correlation Analysis

    Science.gov (United States)

    Hwang, Heungsun; Jung, Kwanghee; Takane, Yoshio; Woodward, Todd S.

    2012-01-01

    We propose functional multiple-set canonical correlation analysis for exploring associations among multiple sets of functions. The proposed method includes functional canonical correlation analysis as a special case when only two sets of functions are considered. As in classical multiple-set canonical correlation analysis, computationally, the…

  14. Bosonic Partition Functions

    CERN Document Server

    Kellerstein, M; Verbaarschot, J J M

    2016-01-01

    The behavior of quenched Dirac spectra of two-dimensional lattice QCD is consistent with spontaneous chiral symmetry breaking which is forbidden according to the Coleman-Mermin-Wagner theorem. One possible resolution of this paradox is that, because of the bosonic determinant in the partially quenched partition function, the conditions of this theorem are violated allowing for spontaneous symmetry breaking in two dimensions or less. This goes back to work by Niedermaier and Seiler on nonamenable symmetries of the hyperbolic spin chain and earlier work by two of the auhtors on bosonic partition functions at nonzero chemical potential. In this talk we discuss chiral symmetry breaking for the bosonic partition function of QCD at nonzero isospin chemical potential and a bosonic random matrix theory at imaginary chemical potential and compare the results with the fermionic counterpart. In both cases the chiral symmetry group of the bosonic partition function is noncompact.

  15. Partition density functional theory

    Science.gov (United States)

    Nafziger, Jonathan

    Partition density functional theory (PDFT) is a method for dividing a molecular electronic structure calculation into fragment calculations. The molecular density and energy corresponding to Kohn Sham density-functional theory (KS-DFT) may be exactly recovered from these fragments. Each fragment acts as an isolated system except for the influence of a global one-body 'partition' potential which deforms the fragment densities. In this work, the developments of PDFT are put into the context of other fragment-based density functional methods. We developed three numerical implementations of PDFT: One within the NWChem computational chemistry package using basis sets, and the other two developed from scratch using real-space grids. It is shown that all three of these programs can exactly reproduce a KS-DFT calculation via fragment calculations. The first of our in-house codes handles non-interacting electrons in arbitrary one-dimensional potentials with any number of fragments. This code is used to explore how the exact partition potential changes for different partitionings of the same system and also to study features which determine which systems yield non-integer PDFT occupations and which systems are locked into integer PDFT occupations. The second in-house code, CADMium, performs real-space calculations of diatomic molecules. Features of the exact partition potential are studied for a variety of cases and an analytical formula determining singularities in the partition potential is derived. We introduce an approximation for the non-additive kinetic energy and show how this quantity can be computed exactly. Finally a PDFT functional is developed to address the issues of static correlation and delocalization errors in approximations within DFT. The functional is applied to the dissociation of H2 + and H2.

  16. Matrix string partition function

    CERN Document Server

    Kostov, Ivan K; Kostov, Ivan K.; Vanhove, Pierre

    1998-01-01

    We evaluate quasiclassically the Ramond partition function of Euclidean D=10 U(N) super Yang-Mills theory reduced to a two-dimensional torus. The result can be interpreted in terms of free strings wrapping the space-time torus, as expected from the point of view of Matrix string theory. We demonstrate that, when extrapolated to the ultraviolet limit (small area of the torus), the quasiclassical expressions reproduce exactly the recently obtained expression for the partition of the completely reduced SYM theory, including the overall numerical factor. This is an evidence that our quasiclassical calculation might be exact.

  17. Functional linear regression via canonical analysis

    CERN Document Server

    He, Guozhong; Wang, Jane-Ling; Yang, Wenjing; 10.3150/09-BEJ228

    2011-01-01

    We study regression models for the situation where both dependent and independent variables are square-integrable stochastic processes. Questions concerning the definition and existence of the corresponding functional linear regression models and some basic properties are explored for this situation. We derive a representation of the regression parameter function in terms of the canonical components of the processes involved. This representation establishes a connection between functional regression and functional canonical analysis and suggests alternative approaches for the implementation of functional linear regression analysis. A specific procedure for the estimation of the regression parameter function using canonical expansions is proposed and compared with an established functional principal component regression approach. As an example of an application, we present an analysis of mortality data for cohorts of medflies, obtained in experimental studies of aging and longevity.

  18. Partial domain wall partition functions

    OpenAIRE

    Foda, O.; Wheeler, M.

    2012-01-01

    We consider six-vertex model configurations on an n-by-N lattice, n =< N, that satisfy a variation on domain wall boundary conditions that we define and call "partial domain wall boundary conditions". We obtain two expressions for the corresponding "partial domain wall partition function", as an (N-by-N)-determinant and as an (n-by-n)-determinant. The latter was first obtained by I Kostov. We show that the two determinants are equal, as expected from the fact that they are partition functions...

  19. On higher spin partition functions

    CERN Document Server

    Beccaria, M

    2015-01-01

    We observe that the partition function of the set of all free massless higher spins s=0,1,2,3,... in flat space is equal to one: the ghost determinants cancel against the "physical" ones or, equivalently, the (regularized) total number of degrees of freedom vanishes. This reflects large underlying gauge symmetry and suggests analogy with supersymmetric or topological theory. The Z=1 property extends also to the AdS background, i.e. the 1-loop vacuum partition function of Vasiliev theory is equal to 1 (assuming a particular regularization of the sum over spins); this was noticed earlier as a consistency requirement for the vectorial AdS/CFT duality. We find that Z=1 is also true in the conformal higher spin theory (with higher-derivative d^{2s} kinetic terms) expanded near flat or conformally flat S^4 background. We also consider the partition function of free conformal theory of symmetric traceless rank s tensor field which has 2-derivative kinetic term but only scalar gauge invariance in flat space. This non...

  20. Evaluation of the grand-canonical partition function using expanded Wang-Landau simulations. IV. Performance of many-body force fields and tight-binding schemes for the fluid phases of silicon.

    Science.gov (United States)

    Desgranges, Caroline; Delhommelle, Jerome

    2016-03-28

    We extend Expanded Wang-Landau (EWL) simulations beyond classical systems and develop the EWL method for systems modeled with a tight-binding Hamiltonian. We then apply the method to determine the partition function and thus all thermodynamic properties, including the Gibbs free energy and entropy, of the fluid phases of Si. We compare the results from quantum many-body (QMB) tight binding models, which explicitly calculate the overlap between the atomic orbitals of neighboring atoms, to those obtained with classical many-body (CMB) force fields, which allow to recover the tetrahedral organization in condensed phases of Si through, e.g., a repulsive 3-body term that favors the ideal tetrahedral angle. Along the vapor-liquid coexistence, between 3000 K and 6000 K, the densities for the two coexisting phases are found to vary significantly (by 5 orders of magnitude for the vapor and by up to 25% for the liquid) and to provide a stringent test of the models. Transitions from vapor to liquid are predicted to occur for chemical potentials that are 10%-15% higher for CMB models than for QMB models, and a ranking of the force fields is provided by comparing the predictions for the vapor pressure to the experimental data. QMB models also reveal the formation of a gap in the electronic density of states of the coexisting liquid at high temperatures. Subjecting Si to a nanoscopic confinement has a dramatic effect on the phase diagram with, e.g. at 6000 K, a decrease in liquid densities by about 50% for both CMB and QMB models and an increase in vapor densities between 90% (CMB) and 170% (QMB). The results presented here provide a full picture of the impact of the strategy (CMB or QMB) chosen to model many-body effects on the thermodynamic properties of the fluid phases of Si.

  1. Partition functions for supersymmetric black holes

    NARCIS (Netherlands)

    J. Manschot

    2008-01-01

    This thesis presents a number of results on partition functions for four-dimensional supersymmetric black holes. These partition functions are important tools to explain the entropy of black holes from a microscopic point of view. Such a microscopic explanation was desired after the association of a

  2. Partial domain wall partition functions

    CERN Document Server

    Foda, O

    2012-01-01

    We consider six-vertex model configurations on a rectangular lattice with n (N) horizontal (vertical) lines, and "partial domain wall boundary conditions" defined as 1. all 2n arrows on the left and right boundaries point inwards, 2. n_u (n_l) arrows on the upper (lower) boundary, such that n_u + n_l = N - n, also point inwards, 3. all remaining n+N arrows on the upper and lower boundaries point outwards, and 4. all spin configurations on the upper and lower boundaries are summed over. To generate (n-by-N) "partial domain wall configurations", one can start from A. (N-by-N) configurations with domain wall boundary conditions and delete n_u (n_l) upper (lower) horizontal lines, or B. (2n-by-N) configurations that represent the scalar product of an n-magnon Bethe eigenstate and an n-magnon generic state on an N-site spin-1/2 chain, and delete the n lines that represent the Bethe eigenstate. The corresponding "partial domain wall partition function" is computed in construction {A} ({B}) as an N-by-N (n-by-n) det...

  3. Reinforcement learning with partitioning function system

    Institute of Scientific and Technical Information of China (English)

    李伟; 叶庆泰; 朱昌明

    2004-01-01

    The size of state-space is the limiting factor in applying reinforcement learning algorithms to practical cases. A reinforcement learning system with partitioning function (RLWPF) is established, in which statespace is partitioned into several regions. Inside the performance principle of RLWPF is based on a Semi-Markov decision process and has general significance. It can be applied to any reinforcement learning with a large statespace. In RLWPF, the partitioning module dispatches agents into different regions in order to decrease the state-space of each agent. This article proves the convergence of the SARSA algorithm for a Semi-Markov decision process, ensuring the convergence of RLWPF by analyzing the equivalence of two value functions in two Semi-Markov decision processes before and after partitioning. This article can show that the optimal policy learned by RLWPF is consistent with prior domain knowledge. An elevator group system is devised to decrease the average waiting time of passengers. Four agents control four elevator cars respectively. Based on RLWPF, a partitioning module is developed through defining a uniform round trip time as the partitioning criteria, making the wait time of most passengers more or less identical then elevator cars should only answer hall calls in their own region. Compared with ordinary elevator systems and reinforcement learning systems without partitioning module, the performance results show the advantage of RLWPF.

  4. Partition function of free conformal higher spin theory

    CERN Document Server

    Beccaria, Matteo; Tseytlin, Arkady A

    2014-01-01

    We compute the canonical partition function Z of non-interacting conformal higher spin (CHS) theory viewed as a collection of free spin s CFT's in R^d. We discuss in detail the 4-dimensional case (where s=1 is the standard Maxwell vector, s=2 is the Weyl graviton, etc.), but also present a generalization for all even dimensions d. Z may be found by counting the numbers of conformal operators and their descendants (modulo gauge identities and equations of motion) weighted by scaling dimensions. This conformal operator counting method requires a careful analysis of the structure of characters of relevant (conserved current, shadow field and conformal Killing tensor) representations of the conformal algebra so(d,2). There is also a close relation to massless higher spin partition functions with alternative boundary conditions in AdS_{d+1}. The same partition function Z may also be computed from the CHS path integral on a curved S^1 x S^{d-1} background. This allows us to determine a simple factorized form of the...

  5. Derivation of Mayer Series from Canonical Ensemble

    Science.gov (United States)

    Wang, Xian-Zhi

    2016-02-01

    Mayer derived the Mayer series from both the canonical ensemble and the grand canonical ensemble by use of the cluster expansion method. In 2002, we conjectured a recursion formula of the canonical partition function of a fluid (X.Z. Wang, Phys. Rev. E 66 (2002) 056102). In this paper we give a proof for this formula by developing an appropriate expansion of the integrand of the canonical partition function. We further derive the Mayer series solely from the canonical ensemble by use of this recursion formula.

  6. Partition Function of Interacting Calorons Ensemble

    CERN Document Server

    Deldar, Sedigheh

    2015-01-01

    We present a method for computing the partition function of a caloron ensemble taking into account the interaction of calorons. We focus on caloron-Dirac string interaction and show that the metric that Diakonov and Petrov offered works well in the limit where this interaction occurs. We suggest computing the correlation function of two polyakov loops by applying Ewald's method.

  7. Partition function of interacting calorons ensemble

    Science.gov (United States)

    Deldar, S.; Kiamari, M.

    2016-01-01

    We present a method for computing the partition function of a caloron ensemble taking into account the interaction of calorons. We focus on caloron-Dirac string interaction and show that the metric that Diakonov and Petrov offered, works well in the limit where this interaction occurs. We suggest computing the correlation function of two polyakov loops by applying Ewald's method.

  8. Domain wall partition functions and KP

    International Nuclear Information System (INIS)

    We observe that the partition function of the six-vertex model on a finite square lattice with domain wall boundary conditions is (a restriction of) a KP τ function and express it as an expectation value of charged free fermions (up to an overall normalization)

  9. Domain wall partition functions and KP

    CERN Document Server

    Foda, O; Zuparic, M

    2009-01-01

    We observe that the partition function of the six vertex model on a finite square lattice with domain wall boundary conditions is (a restriction of) a KP tau function and express it as an expectation value of charged free fermions (up to an overall normalization).

  10. Partition functions and graphs: A combinatorial approach

    CERN Document Server

    Solomon, A I; Duchamp, G; Horzela, A; Penson, K A; Solomon, Allan I.; Blasiak, Pawel; Duchamp, Gerard; Horzela, Andrzej; Penson, Karol A.

    2004-01-01

    Although symmetry methods and analysis are a necessary ingredient in every physicist's toolkit, rather less use has been made of combinatorial methods. One exception is in the realm of Statistical Physics, where the calculation of the partition function, for example, is essentially a combinatorial problem. In this talk we shall show that one approach is via the normal ordering of the second quantized operators appearing in the partition function. This in turn leads to a combinatorial graphical description, giving essentially Feynman-type graphs associated with the theory. We illustrate this methodology by the explicit calculation of two model examples, the free boson gas and a superfluid boson model. We show how the calculation of partition functions can be facilitated by knowledge of the combinatorics of the boson normal ordering problem; this naturally gives rise to the Bell numbers of combinatorics. The associated graphical representation of these numbers gives a perturbation expansion in terms of a sequen...

  11. Some reference formulas for the generating functions of canonical transformations

    Energy Technology Data Exchange (ETDEWEB)

    Anselmi, Damiano [Universita di Pisa, Dipartimento di Fisica ' ' Enrico Fermi' ' , Pisa (Italy); INFN, Sezione di Pisa, Pisa (Italy)

    2016-02-15

    We study some properties of the canonical transformations in classical mechanics and quantum field theory and give a number of practical formulas concerning their generating functions. First, we give a diagrammatic formula for the perturbative expansion of the composition law around the identity map. Then we propose a standard way to express the generating function of a canonical transformation by means of a certain ''componential'' map, which obeys the Baker-Campbell-Hausdorff formula. We derive the diagrammatic interpretation of the componential map, work out its relation with the solution of the Hamilton-Jacobi equation and derive its time-ordered version. Finally, we generalize the results to the Batalin-Vilkovisky formalism, where the conjugate variables may have both bosonic and fermionic statistics, and describe applications to quantum field theory. (orig.)

  12. Some reference formulas for the generating functions of canonical transformations

    International Nuclear Information System (INIS)

    We study some properties of the canonical transformations in classical mechanics and quantum field theory and give a number of practical formulas concerning their generating functions. First, we give a diagrammatic formula for the perturbative expansion of the composition law around the identity map. Then we propose a standard way to express the generating function of a canonical transformation by means of a certain ''componential'' map, which obeys the Baker-Campbell-Hausdorff formula. We derive the diagrammatic interpretation of the componential map, work out its relation with the solution of the Hamilton-Jacobi equation and derive its time-ordered version. Finally, we generalize the results to the Batalin-Vilkovisky formalism, where the conjugate variables may have both bosonic and fermionic statistics, and describe applications to quantum field theory. (orig.)

  13. Some reference formulas for the generating functions of canonical transformations

    Science.gov (United States)

    Anselmi, Damiano

    2016-02-01

    We study some properties of the canonical transformations in classical mechanics and quantum field theory and give a number of practical formulas concerning their generating functions. First, we give a diagrammatic formula for the perturbative expansion of the composition law around the identity map. Then we propose a standard way to express the generating function of a canonical transformation by means of a certain "componential" map, which obeys the Baker-Campbell-Hausdorff formula. We derive the diagrammatic interpretation of the componential map, work out its relation with the solution of the Hamilton-Jacobi equation and derive its time-ordered version. Finally, we generalize the results to the Batalin-Vilkovisky formalism, where the conjugate variables may have both bosonic and fermionic statistics, and describe applications to quantum field theory.

  14. Some reference formulas for the generating functions of canonical transformations

    CERN Document Server

    Anselmi, Damiano

    2015-01-01

    We study some properties of the canonical transformations in classical mechanics and quantum field theory and give a number of practical formulas concerning their generating functions. First, we give a diagrammatic formula for the perturbative expansion of the composition law around the identity map. Then, we propose a standard way to express the generating function of a canonical transformation by means of a certain "componential" map, which obeys the Baker-Campbell-Hausdorff formula. We derive the diagrammatic interpretation of the componential map, work out its relation with the solution of the Hamilton-Jacobi equation and derive its time-ordered version. Finally, we generalize the results to the Batalin-Vilkovisky formalism, where the conjugate variables may have both bosonic and fermionic statistics, and describe applications to quantum field theory.

  15. Indefinite theta functions and black hole partition functions

    International Nuclear Information System (INIS)

    We explore various aspects of supersymmetric black hole partition functions in four-dimensional toroidally compactified heterotic string theory. These functions suffer from divergences owing to the hyperbolic nature of the charge lattice in this theory, which prevents them from having well-defined modular transformation properties. In order to rectify this, we regularize these functions by converting the divergent series into indefinite theta functions, thereby obtaining fully regulated single-centered black hole partitions functions

  16. Indefinite theta functions and black hole partition functions

    Energy Technology Data Exchange (ETDEWEB)

    Cardoso, Gabriel Lopes; Cirafici, Michele [Center for Mathematical Analysis, Geometry, and Dynamical Systems,Departamento de Matemática and LARSyS, Instituto Superior Técnico,1049-001 Lisboa (Portugal); Jorge, Rogério [Instituto Superior Técnico,1049-001 Lisboa (Portugal); Nampuri, Suresh [Laboratoire de Physique Théorique, École Normale Supérieure,24 rue Lhomond, 75231 Paris Cedex 05 (France)

    2014-02-05

    We explore various aspects of supersymmetric black hole partition functions in four-dimensional toroidally compactified heterotic string theory. These functions suffer from divergences owing to the hyperbolic nature of the charge lattice in this theory, which prevents them from having well-defined modular transformation properties. In order to rectify this, we regularize these functions by converting the divergent series into indefinite theta functions, thereby obtaining fully regulated single-centered black hole partitions functions.

  17. Virasoro constraint for Nekrasov instanton partition function

    CERN Document Server

    Kanno, Shoichi; Zhang, Hong

    2012-01-01

    We show that Nekrasov instanton partition function for SU(N) gauge theories satisfies recursion relations in the form of U(1)+Virasoro constraints when {\\beta} = 1. The constraints give a direct support for AGT conjecture for general quiver gauge theories.

  18. Sifting Function Partition for the Goldbach Problem

    CERN Document Server

    Song, Fu-Gao

    2008-01-01

    All sieve methods for the Goldbach problem sift out all the composite numbers; even though, strictly speaking, it is not necessary to do so and which is, in general, very difficult. Some new methods introduced in this paper show that the Goldbach problem can be solved under sifting out only some composite numbers. In fact, in order to prove the Goldbach conjecture, it is only necessary to show that there are prime numbers left in the residual integers after the initial sifting! This idea can be implemented by using one of the three methods called sifting function partition by integer sort, sifting function partition by intervals and comparative sieve method, respectively. These are feasible methods for solving both the Goldbach problem and the problem of twin primes. An added bonus of the above methods is the elimination of the indeterminacy of the sifting functions brought about by their upper and lower bounds.

  19. Parametric Potential Determination by the Canonical Function Method

    CERN Document Server

    Tannous, C; Langlois, J M

    1999-01-01

    The canonical function method (CFM) is a powerful means for solving the Radial Schrodinger Equation. The mathematical difficulty of the RSE lies in the fact it is a singular boundary value problem. The CFM turns it into a regular initial value problem and allows the full determination of the spectrum of the Schrodinger operator without calculating the eigenfunctions. Following the parametrisation suggested by Klapisch and Green, Sellin and Zachor we develop a CFM to optimise the potential parameters in order to reproduce the experimental Quantum Defect results for various Rydberg series of He, Ne and Ar as evaluated from Moore's data.

  20. Supersymmetric partition functions on Riemann surfaces

    CERN Document Server

    Benini, Francesco

    2016-01-01

    We present a compact formula for the supersymmetric partition function of 2d N=(2,2), 3d N=2 and 4d N=1 gauge theories on $\\Sigma_g \\times T^n$ with partial topological twist on $\\Sigma_g$, where $\\Sigma_g$ is a Riemann surface of arbitrary genus and $T^n$ is a torus with n=0,1,2, respectively. In 2d we also include certain local operator insertions, and in 3d we include Wilson line operator insertions along $S^1$. For genus g=1, the formula computes the Witten index. We present a few simple Abelian and non-Abelian examples, including new tests of non-perturbative dualities. We also show that the large N partition function of ABJM theory on $\\Sigma_g \\times S^1$ reproduces the Bekenstein-Hawking entropy of BPS black holes in AdS4 whose horizon has $\\Sigma_g$ topology.

  1. Scalable Semisupervised Functional Neurocartography Reveals Canonical Neurons in Behavioral Networks.

    Science.gov (United States)

    Frady, E Paxon; Kapoor, Ashish; Horvitz, Eric; Kristan, William B

    2016-08-01

    Large-scale data collection efforts to map the brain are underway at multiple spatial and temporal scales, but all face fundamental problems posed by high-dimensional data and intersubject variability. Even seemingly simple problems, such as identifying a neuron/brain region across animals/subjects, become exponentially more difficult in high dimensions, such as recognizing dozens of neurons/brain regions simultaneously. We present a framework and tools for functional neurocartography-the large-scale mapping of neural activity during behavioral states. Using a voltage-sensitive dye (VSD), we imaged the multifunctional responses of hundreds of leech neurons during several behaviors to identify and functionally map homologous neurons. We extracted simple features from each of these behaviors and combined them with anatomical features to create a rich medium-dimensional feature space. This enabled us to use machine learning techniques and visualizations to characterize and account for intersubject variability, piece together a canonical atlas of neural activity, and identify two behavioral networks. We identified 39 neurons (18 pairs, 3 unpaired) as part of a canonical swim network and 17 neurons (8 pairs, 1 unpaired) involved in a partially overlapping preparatory network. All neurons in the preparatory network rapidly depolarized at the onsets of each behavior, suggesting that it is part of a dedicated rapid-response network. This network is likely mediated by the S cell, and we referenced VSD recordings to an activity atlas to identify multiple cells of interest simultaneously in real time for further experiments. We targeted and electrophysiologically verified several neurons in the swim network and further showed that the S cell is presynaptic to multiple neurons in the preparatory network. This study illustrates the basic framework to map neural activity in high dimensions with large-scale recordings and how to extract the rich information necessary to perform

  2. Modular properties of full 5D SYM partition function

    CERN Document Server

    Qiu, Jian; Winding, Jacob; Zabzine, Maxim

    2015-01-01

    We study properties of the full partition function for the $U(1)$ 5D $\\mathcal{N}=2^*$ gauge theory with adjoint hypermultiplet of mass $M$. This theory is ultimately related to abelian 6D (2,0) theory. We construct the full non-perturbative partition function on toric Sasaki-Einstein manifolds by gluing flat copies of the Nekrasov partition function and we express the full partition function in terms of the generalized double elliptic gamma function $G_2^C$ associated with a certain moment map cone $C$. The answer exhibits a curious $SL(4,\\mathbb{Z})$ modular property. Finally, we propose a set of rules to construct the partition function that resembles the calculation of 5D supersymmetric partition function with the insertion of defects of various co-dimensions.

  3. Modular properties of full 5D SYM partition function

    Science.gov (United States)

    Qiu, Jian; Tizzano, Luigi; Winding, Jacob; Zabzine, Maxim

    2016-03-01

    We study properties of the full partition function for the U(1) 5D N = {2}^{ast } gauge theory with adjoint hypermultiplet of mass M . This theory is ultimately related to abelian 6D (2,0) theory. We construct the full non-perturbative partition function on toric Sasaki-Einstein manifolds by gluing flat copies of the Nekrasov partition function and we express the full partition function in terms of the generalized double elliptic gamma function G 2 C associated with a certain moment map cone C. The answer exhibits a curious SL(4 , ℤ) modular property. Finally, we propose a set of rules to construct the partition function that resembles the calculation of 5d supersymmetric partition function with the insert ion of defects of various co-dimensions.

  4. On the canonical decomposition of generalized modular functions

    CERN Document Server

    Kohnen, Winfried

    2010-01-01

    The authors have conjectured (\\cite{KoM}) that if a normalized generalized modular function (GMF) $f$, defined on a congruence subgroup $\\Gamma$, has integral Fourier coefficients, then $f$ is classical in the sense that some power $f^m$ is a modular function on $\\Gamma$. A strengthened form of this conjecture was proved (loc cit) in case the divisor of $f$ is \\emph{empty}. In the present paper we study the canonical decomposition of a normalized parabolic GMF $f = f_1f_0$ into a product of normalized parabolic GMFs $f_1, f_0$ such that $f_1$ has \\emph{unitary character} and $f_0$ has \\emph{empty divisor}. We show that the strengthened form of the conjecture holds if the first "few" Fourier coefficients of $f_1$ are algebraic. We deduce proofs of several new cases of the conjecture, in particular if either $f_0=1$ or if the divisor of $f$ is concentrated at the cusps of $\\Gamma$.

  5. Partition function of nearest neighbour Ising models: Some new insights

    Indian Academy of Sciences (India)

    G Nandhini; M V Sangaranarayanan

    2009-09-01

    The partition function for one-dimensional nearest neighbour Ising models is estimated by summing all the energy terms in the Hamiltonian for N sites. The algebraic expression for the partition function is then employed to deduce the eigenvalues of the basic 2 × 2 matrix and the corresponding Hermitian Toeplitz matrix is derived using the Discrete Fourier Transform. A new recurrence relation pertaining to the partition function for two-dimensional Ising models in zero magnetic field is also proposed.

  6. Semiclassical limits of quantum partition functions on infinite graphs

    Energy Technology Data Exchange (ETDEWEB)

    Güneysu, Batu, E-mail: gueneysu@math.hu-berlin.de [Institut für Mathematik, Humboldt-Universität zu Berlin, Berlin (Germany)

    2015-02-15

    We prove that if H denotes the operator corresponding to the canonical Dirichlet form on a possibly locally infinite weighted graph (X, b, m), and if v : X → ℝ is such that H + v/ħ is well-defined as a form sum for all ħ > 0, then the quantum partition function tr(e{sup −βħ(H+v/ħ)}) converges to ∑{sub x∈X}e{sup −βv(x)} as ħ → 0 +, for all β > 0, regardless of the fact whether e{sup −βv} is a priori summable or not. This fact can be interpreted as a semiclassical limit, and it allows geometric Weyl-type convergence results. We also prove natural generalizations of this semiclassical limit to a large class of covariant Schrödinger operators that act on sections in Hermitian vector bundle over (X, m, b), a result that particularly applies to magnetic Schrödinger operators that are defined on (X, m, b)

  7. Superconformal indices and partition functions for supersymmetric field theories

    Energy Technology Data Exchange (ETDEWEB)

    Gahramanov, I.B. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Vartanov, G.S. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

    2012-12-15

    Recently there was a substantial progress in understanding of supersymmetric theories (in particular, their BPS spectrum) in space-times of different dimensions due to the exact computation of superconformal indices and partition functions using localization method. Here we discuss a connection of 4d superconformal indices and 3d partition functions using a particular example of supersymmetric theories with matter in antisymmetric representation.

  8. Congruences involving F-partition functions

    Directory of Open Access Journals (Sweden)

    James Sellers

    1994-01-01

    Full Text Available The primary goal of this note is to prove the congruence ϕ3(3n+2≡0(mod3, where ϕ3(n denotes the number of F-partitions of n with at most 3 repetitions. Secondarily, we conjecture a new family of congruences involving cϕ2(n, the number of F-partitions of n with 2 colors.

  9. A canonical correlation neural network for multicollinearity and functional data.

    Science.gov (United States)

    Gou, Zhenkun; Fyfe, Colin

    2004-03-01

    We review a recent neural implementation of Canonical Correlation Analysis and show, using ideas suggested by Ridge Regression, how to make the algorithm robust. The network is shown to operate on data sets which exhibit multicollinearity. We develop a second model which not only performs as well on multicollinear data but also on general data sets. This model allows us to vary a single parameter so that the network is capable of performing Partial Least Squares regression (at one extreme) to Canonical Correlation Analysis (at the other)and every intermediate operation between the two. On multicollinear data, the parameter setting is shown to be important but on more general data no particular parameter setting is required. Finally, we develop a second penalty term which acts on such data as a smoother in that the resulting weight vectors are much smoother and more interpretable than the weights without the robustification term. We illustrate our algorithms on both artificial and real data.

  10. Bosonic Partition Functions at Nonzero (Imaginary) Chemical Potential

    CERN Document Server

    Kellerstein, M

    2016-01-01

    We consider bosonic random matrix partition functions at nonzero chemical potential and compare the chiral condensate, the baryon number density and the baryon number susceptibility to the result of the corresponding fermionic partition function. We find that as long as results are finite, the phase transition of the fermionic theory persists in the bosonic theory. However, in case that bosonic partition function diverges and has to be regularized, the phase transition of the fermionic theory does not occur in the bosonic theory, and the bosonic theory is always in the broken phase.

  11. Graph theory and Pfaffian representations of Ising partition function

    OpenAIRE

    Gobron, Thierry

    2013-01-01

    48 pages A well known theorem due to Kasteleyn states that the partition function of an Ising model on an arbitrary planar graph can be represented as the Pfaffian of a skew-symmetric matrix associated to the graph. This results both embodies the free fermionic nature of any planar Ising model and eventually gives an effective way of computing its partition functions in closed form. An extension of this result to non planar models expresses the partition function as a sum of Pfaffians whic...

  12. String partition functions in Rindler space and maximal acceleration

    CERN Document Server

    Mertens, Thomas G; Zakharov, Valentin I

    2015-01-01

    We revisit non-interacting string partition functions in Rindler space by summing over fields in the spectrum. Using recent results of JHEP 1505 (2015) 106, this construction, first done by Emparan, can be put on much firmer ground. For open strings, we demonstrate that surface contributions to the higher spin fields correspond to open strings piercing the Rindler origin, unifying the higher spin surface contributions in string language. We generalize the construction of these partition functions to type II and heterotic superstrings and demonstrate modular invariance for the resulting partition functions. Also, explicit signs of spacetime supersymmetry are visible. All of these exhibit an IR divergence that can be interpreted as a maximal acceleration with $T_{\\text{crit}} = T_{H}/\\pi$ close to the black hole horizon. Ultimately, these partition functions are not physical, and divergences here should not be viewed as a failure of string theory: maximal acceleration is a feature of a faulty treatment of the h...

  13. On the parity of generalized partition functions, III.

    OpenAIRE

    Ben Said, Fethi; Nicolas, Jean-Louis; Zekraoui, Ahlem

    2010-01-01

    International audience Improving on some results of J.-L. Nicolas, the elements of the set ${\\cal A}={\\cal A}(1+z+z^3+z^4+z^5)$, for which the partition function $p({\\cal A},n)$ (i.e. the number of partitions of $n$ with parts in ${\\cal A}$) is even for all $n\\geq 6$ are determined. An asymptotic estimate to the counting function of this set is also given.

  14. A brief history of partitions of numbers, partition functions and their modern applications

    Science.gov (United States)

    Debnath, Lokenath

    2016-04-01

    'Number rules the universe.' The Pythagoras 'If you wish to forsee the future of mathematics our course is to study the history and present conditions of the science.' Henri Poincaré 'The primary source (Urqell) of all mathematics are integers.' Hermann Minkowski This paper is written to commemorate the centennial anniversary of the Mathematical Association of America. It deals with a short history of different kinds of natural numbers including triangular, square, pentagonal, hexagonal and k-gonal numbers, and their simple properties and their geometrical representations. Included are Euclid's and Pythagorean's main contributions to elementary number theory with the main contents of the Euclid Elements of the 13-volume masterpiece of mathematical work. This is followed by Euler's new discovery of the additive number theory based on partitions of numbers. Special attention is given to many examples, Euler's theorems on partitions of numbers with geometrical representations of Ferrers' graphs, Young's diagrams, Lagrange's four-square theorem and the celebrated Waring problem. Included are Euler's generating functions for the partitions of numbers, Euler's pentagonal number theorem, Gauss' triangular and square number theorems and the Jacobi triple product identity. Applications of the theory of partitions of numbers to different statistics such as the Bose- Einstein, Fermi- Dirac, Gentile, and Maxwell- Boltzmann statistics are briefly discussed. Special attention is given to pedagogical information through historical approach to number theory so that students and teachers at the school, college and university levels can become familiar with the basic concepts of partitions of numbers, partition functions and their modern applications, and can pursue advanced study and research in analytical and computational number theory.

  15. Line defects and 5d instanton partition functions

    Science.gov (United States)

    Kim, Hee-Cheol

    2016-03-01

    We consider certain line defect operators in five-dimensional SUSY gauge theories, whose interaction with the self-dual instantons is described by 1d ADHM-like gauged quantum mechanics constructed by Tong and Wong. The partition function in the presence of these operators is known to be a generating function of BPS Wilson loops in skew symmetric tensor representations of the gauge group. We calculate the partition function and explicitly prove that it is a finite polynomial of the defect mass parameter x, which is an essential property of the defect operator and the Wilson loop generating function. The relation between the line defect partition function and the qq-character defined by N . Nekrasov is briefly discussed.

  16. Line defects and 5d instanton partition functions

    CERN Document Server

    Kim, Hee-Cheol

    2016-01-01

    We consider certain line defect operators in five-dimensional SUSY gauge theories, whose interaction with the self-dual instantons is described by 1d ADHM-like gauged quantum mechanics constructed by Tong and Wong. The partition function in the presence of these operators is known to be a generating function of BPS Wilson loops in skew symmetric tensor representations of the gauge group. We calculate the partition function and explicitly prove that it is a finite polynomial of the defect mass parameter $x$, which is an essential property of the defect operator and the Wilson loop generating function. The relation between the line defect partition function and the qq-character defined by N. Nekrasov is briefly discussed.

  17. Grand canonical potential of a magnetized neutron gas

    CERN Document Server

    Diener, Jacobus P W

    2015-01-01

    We compute the effective action for stationary and spatially constant magnetic fields, when coupled anomalously to charge neutral fermions, by integrating out the fermions. From this the grand canonical partition function and potential of the fermions and fields are computed. This also takes care of magnetic field dependent vacuum corrections to the grand canonical potential. Possible applications to neutron stars are indicated.

  18. Asymptotics of a singularly perturbed GUE partition function

    CERN Document Server

    Mezzadri, F

    2010-01-01

    We study the double scaling asymptotic limit for large matrix dimension N of the partition function of the unitary ensemble with weight exp(-z^2/2x^2 + t/x - x^2/2). We derive the asymptotics of the partition function when z and t are of O(N^(-1/2)). Our results are obtained using the Deift-Zhou steepest descent method and are expressed in terms of a solution of a fourth order nonlinear differential equation. We also compute the asymptotic limit of such a solution when zN^(1/2) -> 0. The behavior of this solution, together with fact that the partition function is an odd function in the variable t, allows us to reduce such a fourth order differential equation into a second order nonlinear ODE.

  19. Partition function of massless scalar field in Schwarzschild background

    CERN Document Server

    Sanyal, Abhik Kumar

    2014-01-01

    Using thermal value of zeta function instead of zero temperature, the partition function of quantized fields in arbitrary stationary backgrounds was found to be independent of undetermined regularization constant in even-dimension and the long drawn problem associated with the trace anomaly effect had been removed. Here, we explicitly calculate the expression for the coincidence limit so that the technique may be applied in some specific problems. A particular problem dealt with here is to calculate the partition function of massless scalar field in Schwarzschild background.

  20. Graphs of partitions and Ramanujan's tau-function

    OpenAIRE

    Brent, Barry

    2004-01-01

    The invariant z_{lambda} attached to a partition lambda sits in the denominator of the Girard-Waring solution to Newton's symmetric function relations. We interpret Ramanujan's tau-function in terms of z_lambda, and interpret z_lambda in terms of the automorphisms of a graph.

  1. Constraints on Fluid Dynamics from Equilibrium Partition Functions

    CERN Document Server

    Banerjee, Nabamita; Bhattacharyya, Sayantani; Jain, Sachin; Minwalla, Shiraz; Sharma, Tarun

    2012-01-01

    We study the thermal partition function of quantum field theories on arbitrary stationary background spacetime, and with arbitrary stationary background gauge fields, in the long wavelength expansion. We demonstrate that the equations of relativistic hydrodynamics are significantly constrained by the requirement of consistency with any partition function. In examples at low orders in the derivative expansion we demonstrate that these constraints coincide precisely with the equalities between hydrodynamical transport coefficients that follow from the local form of the second law of thermodynamics. In particular we recover the results of Son and Surowka on the chiral magnetic and chiral vorticity flows, starting from a local partition function that manifestly reproduces the field theory anomaly, without making any reference to an entropy current. We conjecture that the relations between transport coefficients that follow from the second law of thermodynamics agree to all orders in the derivative expansion with ...

  2. Approximation methods for the partition functions of anharmonic systems

    Energy Technology Data Exchange (ETDEWEB)

    Lew, P.; Ishida, T.

    1979-07-01

    The analytical approximations for the classical, quantum mechanical and reduced partition functions of the diatomic molecule oscillating internally under the influence of the Morse potential have been derived and their convergences have been tested numerically. This successful analytical method is used in the treatment of anharmonic systems. Using Schwinger perturbation method in the framework of second quantization formulism, the reduced partition function of polyatomic systems can be put into an expression which consists separately of contributions from the harmonic terms, Morse potential correction terms and interaction terms due to the off-diagonal potential coefficients. The calculated results of the reduced partition function from the approximation method on the 2-D and 3-D model systems agree well with the numerical exact calculations.

  3. Approximation methods for the partition functions of anharmonic systems

    International Nuclear Information System (INIS)

    The analytical approximations for the classical, quantum mechanical and reduced partition functions of the diatomic molecule oscillating internally under the influence of the Morse potential have been derived and their convergences have been tested numerically. This successful analytical method is used in the treatment of anharmonic systems. Using Schwinger perturbation method in the framework of second quantization formulism, the reduced partition function of polyatomic systems can be put into an expression which consists separately of contributions from the harmonic terms, Morse potential correction terms and interaction terms due to the off-diagonal potential coefficients. The calculated results of the reduced partition function from the approximation method on the 2-D and 3-D model systems agree well with the numerical exact calculations

  4. Revisiting noninteracting string partition functions in Rindler space

    Science.gov (United States)

    Mertens, Thomas G.; Verschelde, Henri; Zakharov, Valentin I.

    2016-05-01

    We revisit noninteracting string partition functions in Rindler space by summing over fields in the spectrum. In field theory, the total partition function splits in a natural way into a piece that does not contain surface terms and a piece consisting of solely the so-called edge states. For open strings, we illustrate that surface contributions to the higher-spin fields correspond to open strings piercing the Rindler origin, unifying the higher-spin surface contributions in string language. For closed strings, we demonstrate that the string partition function is not quite the same as the sum over the partition functions of the fields in the spectrum: an infinite overcounting is present for the latter. Next we study the partition functions obtained by excluding the surface terms. Using recent results of He et al. [J. High Energy Phys. 05 (2015) 106], this construction, first done by Emparan [arXiv:hep-th/9412003], can be put on much firmer ground. We generalize to type II and heterotic superstrings and demonstrate modular invariance. All of these exhibit an IR divergence that can be interpreted as a maximal acceleration close to the black hole horizon. Ultimately, since these partition functions are only part of the full story, divergences here should not be viewed as a failure of string theory: maximal acceleration is a feature of a faulty treatment of the higher-spin fields in the string spectrum. We comment on the relevance of this to Solodukhin's recent proposal [Phys. Rev. D 91, 084028 (2015)]. A possible link with the firewall paradox is apparent.

  5. Nested sampling of isobaric phase space for the direct evaluation of the isothermal-isobaric partition function of atomic systems

    International Nuclear Information System (INIS)

    Nested Sampling (NS) is a powerful athermal statistical mechanical sampling technique that directly calculates the partition function, and hence gives access to all thermodynamic quantities in absolute terms, including absolute free energies and absolute entropies. NS has been used predominately to compute the canonical (NVT) partition function. Although NS has recently been used to obtain the isothermal-isobaric (NPT) partition function of the hard sphere model, a general approach to the computation of the NPT partition function has yet to be developed. Here, we describe an isobaric NS (IBNS) method which allows for the computation of the NPT partition function of any atomic system. We demonstrate IBNS on two finite Lennard-Jones systems and confirm the results through comparison to parallel tempering Monte Carlo. Temperature-entropy plots are constructed as well as a simple pressure-temperature phase diagram for each system. We further demonstrate IBNS by computing part of the pressure-temperature phase diagram of a Lennard-Jones system under periodic boundary conditions

  6. Identification of plasmid partition function in coryneform bacteria.

    OpenAIRE

    Kurusu, Y; Satoh, Y.; Inui, M.; Kohama, K; Kobayashi, M.; Terasawa, M.; Yukawa, H

    1991-01-01

    We have identified and characterized a partition function that is required for stable maintenance of plasmids in the coryneform bacteria Brevibacterium flavum MJ233 and Corynebacterium glutamicum ATCC 31831. This function is localized to a HindIII-NspV fragment (673 bp) adjacent to the replication region of the plasmid, named pBY503, from Brevibacterium stationis IFO 12144. The function was independent of copy number control and was not associated directly with plasmid replication functions. ...

  7. Canonical self-affine tilings by iterated function systems

    OpenAIRE

    Pearse, Erin P. J.

    2006-01-01

    An iterated function system $\\Phi$ consisting of contractive similarity mappings has a unique attractor $F \\subseteq \\mathbb{R}^d$ which is invariant under the action of the system, as was shown by Hutchinson [Hut]. This paper shows how the action of the function system naturally produces a tiling $\\mathcal{T}$ of the convex hull of the attractor. More precisely, it tiles the complement of the attractor within its convex hull. These tiles form a collection of sets whose geometry is typically ...

  8. Partition functions 1: Improved partition functions and thermodynamic quantities for normal, equilibrium, and ortho and para molecular hydrogen

    CERN Document Server

    Popovas, Andrius

    2016-01-01

    Aims. In this work we rigorously show the shortcomings of various simplifications that are used to calculate the total internal partition function. These shortcomings can lead to errors of up to 40 percent or more in the estimated partition function. These errors carry on to calculations of thermodynamic quantities. Therefore a more complicated approach has to be taken. Methods. Seven possible simplifications of various complexity are described, together with advantages and disadvantages of direct summation of experimental values. These were compared to what we consider the most accurate and most complete treatment (case 8). Dunham coefficients were determined from experimental and theoretical energy levels of a number of electronically excited states of H$_2$ . Both equilibrium and normal hydrogen was taken into consideration. Results. Various shortcomings in existing calculations are demonstrated, and the reasons for them are explained. New partition functions for equilibrium, normal, and ortho and para hyd...

  9. Partitions, rooks, and symmetric functions in noncommuting variables

    CERN Document Server

    Can, Mahir Bilen

    2010-01-01

    Let $\\Pi_n$ denote the set of all set partitions of $\\{1,2,\\ldots,n\\}$. We consider two subsets of $\\Pi_n$, one connected to rook theory and one associated with symmetric functions in noncommuting variables. Let $\\cE_n\\sbe\\Pi_n$ be the subset of all partitions corresponding to an extendable rook (placement) on the upper-triangular board, $\\cT_{n-1}$. Given $\\pi\\in\\Pi_m$ and $\\si\\in\\Pi_n$, define their {\\it slash product\\/} to be $\\pi|\\si=\\pi\\cup(\\si+m)\\in\\Pi_{m+n}$ where $\\si+m$ is the partition obtained by adding $m$ to every element of every block of $\\si$. Call $\\tau$ {\\it atomic\\/} if it can not be written as a nontrivial slash product and let $\\cA_n\\sbe\\Pi_n$ denote the subset of atomic partitions. Atomic partitions were first defined by Bergeron, Hohlweg, Rosas, and Zabrocki during their study of $NCSym$, the symmetric functions in noncommuting variables. We show that, despite their very different definitions, $\\cE_n=\\cA_n$ for all $n\\ge0$. Furthermore, we put an algebra structure on the formal vector s...

  10. Zeta Function Expression of Spin Partition Functions on Thermal AdS3

    Directory of Open Access Journals (Sweden)

    Floyd L.Williams

    2015-07-01

    Full Text Available We find a Selberg zeta function expression of certain one-loop spin partition functions on three-dimensional thermal anti-de Sitter space. Of particular interest is the partition function of higher spin fermionic particles. We also set up, in the presence of spin, a Patterson-type formula involving the logarithmic derivative of zeta.

  11. Getting full control of canonical correlation analysis with the AutoBiplot.CCA function

    Science.gov (United States)

    Alves, M. Rui

    2016-06-01

    Function AutoBiplot.CCA was built in R language. Given two multivariate data sets, this function carries out a conventional canonical correlation analysis, followed by the automatic production of predictive biplots based on the accuracy of readings as assessed by a mean standard predictive error and a user defined tolerance value. As the user's intervention is mainly restricted to the choice of the magnitude of the t.axis value, common misinterpretations, overestimations and adjustments between outputs and personal beliefs are avoided.

  12. Analytical functions in non-canonical two dimensional algebras; Funzioni analitiche nelle algebre a due componenti

    Energy Technology Data Exchange (ETDEWEB)

    Catoni, Francesco; Zampetti, Paolo [ENEA, Centro Ricerche Casaccia, Rome (Italy). Dipt. Energia; Cannata, Roberto [ENEA, Centro Ricerche Casaccia, Rome (Italy). Funzione Centrale INFO; Nichelatti, Enrico [ENEA, Centro Ricerche Casaccia, Rome (Italy). Dipt. Innovazione

    1997-10-01

    Systems of two-dimensional hypercomplex numbers are usually studied in their canonical form, i.e. according to the multiplicative rule for the ``imaginary``versor i{sup 2} = {+-} 1, 0. In this report those systems for which i{sup 2} = {alpha} + {beta}i are studied and expressions are derived for functions given by series expansion as well as for some elementary functions. The results obtained for systems which can be decomposed are then extended to all systems.

  13. $q$-Virasoro modular double and 3d partition functions

    CERN Document Server

    Nedelin, Anton; Zabzine, Maxim

    2016-01-01

    We study partition functions of 3d $\\mathcal{N}=2$ U(N) gauge theories on compact manifolds which are $S^1$ fibrations over $S^2$. We show that the partition functions are free field correlators of vertex operators and screening charges of the $q$-Virasoro modular double, which we define. The inclusion of supersymmetric Wilson loops in arbitrary representations allows us to show that the generating functions of Wilson loop vacuum expectation values satisfy two SL(2,$\\mathbb{Z}$)-related commuting sets of $q$-Virasoro constraints. We generalize our construction to 3d $\\mathcal{N}=2$ unitary quiver gauge theories and as an example we give the free boson realization of the ABJ(M) model.

  14. Combinatorics of the three-parameter PASEP partition function

    CERN Document Server

    Josuat-Vergès, Matthieu

    2009-01-01

    We consider a partially asymmetric exclusion process (PASEP) on a finite number of sites with open and directed boundary conditions. Its partition function was calculated by Blythe, Evans, Colaiori, and Essler. It is known to be a generating function of permutation tableaux by the combinatorial interpretation of Corteel and Williams. We prove bijectively two new combinatorial interpretations. The first one is in terms of weighted Motzkin paths called Laguerre histories and is obtained by refining a bijection of Foata and Zeilberger. Secondly we show that this partition function is the generating function of permutations with respect to right-to-left minima, right-to-left maxima, ascents, and 31-2 patterns, by refining a bijection of Francon and Viennot. Then we give a new formula for the partition function which generalizes the one of Blythe & al. It is proved in two combinatorial ways. The first proof is an enumeration of lattice paths which are known to be a solution of the Matrix Ansatz of Derrida &...

  15. Identification of plasmid partition function in coryneform bacteria

    Energy Technology Data Exchange (ETDEWEB)

    Kurusu, Yasurou; Satoh, Yukie; Inui, Masayuki; Kohama, Keiko; Kobayashi, Miki; Terasawa, Masato; Yukawa, Hideaki (Mitsubishi Petrochemical Co., Ltd., Ibaraki (Japan))

    1991-03-01

    The authors have identified and characterized a partition function that is required for stable maintenance of plasmids in the coryneform bacteria Brevibacterium flavum MJ233 and Corynebacterium glutamicum ATCC 31831. This function is localized to a HindIII-NspV fragment (673 bp) adjacent to the replication region of the plasmid, named pBY503, from Brevibacterium stationis IFO 12144. The function was independent of copy number control and was not associated directly with plasmid replication functions. This fragment was able to stabilize the unstable plasmids in cis but not in trans.

  16. Coding Partitions

    Directory of Open Access Journals (Sweden)

    Fabio Burderi

    2007-05-01

    Full Text Available Motivated by the study of decipherability conditions for codes weaker than Unique Decipherability (UD, we introduce the notion of coding partition. Such a notion generalizes that of UD code and, for codes that are not UD, allows to recover the ``unique decipherability" at the level of the classes of the partition. By tacking into account the natural order between the partitions, we define the characteristic partition of a code X as the finest coding partition of X. This leads to introduce the canonical decomposition of a code in at most one unambiguouscomponent and other (if any totally ambiguouscomponents. In the case the code is finite, we give an algorithm for computing its canonical partition. This, in particular, allows to decide whether a given partition of a finite code X is a coding partition. This last problem is then approached in the case the code is a rational set. We prove its decidability under the hypothesis that the partition contains a finite number of classes and each class is a rational set. Moreover we conjecture that the canonical partition satisfies such a hypothesis. Finally we consider also some relationships between coding partitions and varieties of codes.

  17. High-Temperature Expansion of Supersymmetric Partition Functions

    CERN Document Server

    Ardehali, Arash Arabi; Szepietowski, Phillip

    2015-01-01

    Di Pietro and Komargodski have recently demonstrated a four-dimensional counterpart of Cardy's formula, which gives the leading high-temperature ($\\beta \\rightarrow 0$) behavior of supersymmetric partition functions $Z^{SUSY}(\\beta)$. Focusing on superconformal theories, we elaborate on the subleading contributions to their formula when applied to free chiral and U(1) vector multiplets. In particular, we see that the high-temperature expansion of $\\ln Z^{SUSY}(\\beta)$ terminates at order $\\beta^0$. We also demonstrate how their formula must be modified when applied to SU($N$) toric quiver gauge theories in the planar ($N \\rightarrow \\infty$) limit. Our method for regularizing the one-loop determinants of chiral and vector multiplets helps to clarify the relation between the 4d $\\mathcal{N} = 1$ superconformal index and its corresponding supersymmetric partition function obtained by path-integration.

  18. Computing black hole partition functions from quasinormal modes

    CERN Document Server

    Arnold, Peter; Vaman, Diana

    2016-01-01

    We propose a method of computing one-loop determinants in black hole spacetimes (with emphasis on asymptotically anti-de Sitter black holes) that may be used for numerics when completely-analytic results are unattainable. The method utilizes the expression for one-loop determinants in terms of quasinormal frequencies determined by Denef, Hartnoll and Sachdev in [1]. A necessary ingredient is a refined regularization scheme to regulate the contributions of individual fixed-momentum sectors to the partition function. To this end, we formulate an effective two-dimensional problem in which a natural refinement of standard heat kernel techniques can be used to account for contributions to the partition function at fixed momentum. We test our method in a concrete case by reproducing the scalar one-loop determinant in the BTZ black hole background. We then discuss the application of such techniques to more complicated spacetimes.

  19. Unified approach to partition functions of RNA secondary structures.

    Science.gov (United States)

    Bundschuh, Ralf

    2014-11-01

    RNA secondary structure formation is a field of considerable biological interest as well as a model system for understanding generic properties of heteropolymer folding. This system is particularly attractive because the partition function and thus all thermodynamic properties of RNA secondary structure ensembles can be calculated numerically in polynomial time for arbitrary sequences and homopolymer models admit analytical solutions. Such solutions for many different aspects of the combinatorics of RNA secondary structure formation share the property that the final solution depends on differences of statistical weights rather than on the weights alone. Here, we present a unified approach to a large class of problems in the field of RNA secondary structure formation. We prove a generic theorem for the calculation of RNA folding partition functions. Then, we show that this approach can be applied to the study of the molten-native transition, denaturation of RNA molecules, as well as to studies of the glass phase of random RNA sequences.

  20. Partition functions of web diagrams with an O7$^-$-plane

    CERN Document Server

    Hayashi, Hirotaka

    2016-01-01

    We consider the computation of the topological string partition function for 5-brane web diagrams with an O7$^-$-plane. Since upon quantum resolution of the orientifold plane these diagrams become non-toric web diagrams without the orientifold we are able to apply the topological vertex to obtain the Nekrasov partition function of the corresponding 5d theory. We apply this procedure to the case of 5d $SU(N)$ theories with one hypermultiplet in the antisymmetric representation and to the case of 5d pure $USp(2N)$ theories. For these cases we discuss the dictionary between parameters and moduli of the 5d gauge theory and lengths of 5-branes in the web diagram and moreover we perform comparison of the results obtained via application of the topological vertex and the one obtained via localisation techniques, finding in all instances we consider perfect agreement.

  1. Strong Convergence of Partitioning Estimation for Nonparametric Regression Function under Dependence Samples

    Institute of Scientific and Technical Information of China (English)

    LINGNeng-xiang; DUXue-qiao

    2005-01-01

    In this paper, we study the strong consistency for partitioning estimation of regression function under samples that axe φ-mixing sequences with identically distribution.Key words: nonparametric regression function; partitioning estimation; strong convergence;φ-mixing sequences.

  2. Conformal transformations and the SLE partition function martingale

    OpenAIRE

    Bauer, Michel; Bernard, Denis

    2003-01-01

    We present an implementation in conformal field theory (CFT) of local finite conformal transformations fixing a point. We give explicit constructions when the fixed point is either the origin or the point at infinity. Both cases involve the exponentiation of a Borel subalgebra of the Virasoro algebra. We use this to build coherent state representations and to derive a close analog of Wick's theorem for the Virasoro algebra. This allows to compute the conformal partition function in non trivia...

  3. Anyonic partition functions and windings of planar Brownian motion

    International Nuclear Information System (INIS)

    The computation of the N-cycle Brownian paths contribution FN(α) to the N-anyon partition function is addressed. A detailed numerical analysis based on a random walk on a lattice indicates that FN0(α)=product k=1N-1[1-(N/k)α]. In the paramount three-anyon case, one can show that F3(α) is built by linear states belonging to the bosonic, fermionic, and mixed representations of S3

  4. The partition function of a ferromagnet up to three loops

    Energy Technology Data Exchange (ETDEWEB)

    Hofmann, C P, E-mail: christoph@ucol.mx [Facultad de Ciencias, Universidad de Colima, Bernal Diaz del Castillo 340, Colima, Colima 28045 (Mexico)

    2011-04-01

    The low-temperature behavior of ferromagnets with a spontaneously broken symmetry O(3) {yields} O(2) is analyzed within the perspective of effective Lagrangians. The leading coefficients of the low-temperature expansion for the partition function are calculated up to three loops and the manifestation of the spin-wave interaction in this series is discussed. The effective field theory method has the virtue of being completely systematic and model-independent.

  5. Factorized domain wall partition functions in trigonometric vertex models

    CERN Document Server

    Foda, O; Zuparic, M

    2007-01-01

    We obtain factorized domain wall partition functions for two sets of trigonometric vertex models: 1. The N-state Deguchi-Akutsu models, for N = {2, 3, 4} (and conjecture the result for all N >= 5), and 2. The sl(r+1|s+1) Perk-Schultz models, for {r, s = \\N}, where (given the symmetries of these models) the result is independent of {r, s}.

  6. High-temperature asymptotics of supersymmetric partition functions

    CERN Document Server

    Ardehali, Arash Arabi

    2015-01-01

    We study the partition function of 4d supersymmetric gauge theories with an R-symmetry on Euclidean $S^3\\times S_\\beta^1$, with $S^3$ the unit-radius squashed three-sphere, and $\\beta$ the circumference of the circle. For superconformal theories, this partition function coincides (up to a Casimir energy factor) with the 4d superconformal index. The partition function can be computed exactly using supersymmetric localization of the gauge theory path-integral. It takes the form of an elliptic hypergeometric integral, which may be viewed as a matrix-integral over the moduli space of the holonomies of the gauge fields around $S_\\beta^1$. At high temperatures ($\\beta\\to 0$, corresponding to the hyperbolic limit of the elliptic hypergeometric integral) we obtain from the matrix-integral a quantum effective potential for the holonomies. The effective potential is proportional to the temperature. Therefore the high-temperature limit further localizes the matrix-integral to the locus of the minima of the potential. If...

  7. Generalised partition functions: inferences on phase space distributions

    Science.gov (United States)

    Treumann, Rudolf A.; Baumjohann, Wolfgang

    2016-06-01

    It is demonstrated that the statistical mechanical partition function can be used to construct various different forms of phase space distributions. This indicates that its structure is not restricted to the Gibbs-Boltzmann factor prescription which is based on counting statistics. With the widely used replacement of the Boltzmann factor by a generalised Lorentzian (also known as the q-deformed exponential function, where κ = 1/|q - 1|, with κ, q ∈ R) both the kappa-Bose and kappa-Fermi partition functions are obtained in quite a straightforward way, from which the conventional Bose and Fermi distributions follow for κ → ∞. For κ ≠ ∞ these are subject to the restrictions that they can be used only at temperatures far from zero. They thus, as shown earlier, have little value for quantum physics. This is reasonable, because physical κ systems imply strong correlations which are absent at zero temperature where apart from stochastics all dynamical interactions are frozen. In the classical large temperature limit one obtains physically reasonable κ distributions which depend on energy respectively momentum as well as on chemical potential. Looking for other functional dependencies, we examine Bessel functions whether they can be used for obtaining valid distributions. Again and for the same reason, no Fermi and Bose distributions exist in the low temperature limit. However, a classical Bessel-Boltzmann distribution can be constructed which is a Bessel-modified Lorentzian distribution. Whether it makes any physical sense remains an open question. This is not investigated here. The choice of Bessel functions is motivated solely by their convergence properties and not by reference to any physical demands. This result suggests that the Gibbs-Boltzmann partition function is fundamental not only to Gibbs-Boltzmann but also to a large class of generalised Lorentzian distributions as well as to the corresponding nonextensive statistical mechanics.

  8. Quantum algorithm for an additive approximation of Ising partition functions

    Science.gov (United States)

    Matsuo, Akira; Fujii, Keisuke; Imoto, Nobuyuki

    2014-08-01

    We investigate quantum-computational complexity of calculating partition functions of Ising models. We construct a quantum algorithm for an additive approximation of Ising partition functions on square lattices. To this end, we utilize the overlap mapping developed by M. Van den Nest, W. Dür, and H. J. Briegel [Phys. Rev. Lett. 98, 117207 (2007), 10.1103/PhysRevLett.98.117207] and its interpretation through measurement-based quantum computation (MBQC). We specify an algorithmic domain, on which the proposed algorithm works, and an approximation scale, which determines the accuracy of the approximation. We show that the proposed algorithm performs a nontrivial task, which would be intractable on any classical computer, by showing that the problem that is solvable by the proposed quantum algorithm is BQP-complete. In the construction of the BQP-complete problem coupling strengths and magnetic fields take complex values. However, the Ising models that are of central interest in statistical physics and computer science consist of real coupling strengths and magnetic fields. Thus we extend the algorithmic domain of the proposed algorithm to such a real physical parameter region and calculate the approximation scale explicitly. We found that the overlap mapping and its MBQC interpretation improve the approximation scale exponentially compared to a straightforward constant-depth quantum algorithm. On the other hand, the proposed quantum algorithm also provides partial evidence that there exist no efficient classical algorithm for a multiplicative approximation of the Ising partition functions even on the square lattice. This result supports the observation that the proposed quantum algorithm also performs a nontrivial task in the physical parameter region.

  9. Non-perturbative Nekrasov partition function from string theory

    International Nuclear Information System (INIS)

    We calculate gauge instanton corrections to a class of higher derivative string effective couplings introduced in [1]. We work in Type I string theory compactified on K3×T2 and realise gauge instantons in terms of D5-branes wrapping the internal space. In the field theory limit we reproduce the deformed ADHM action on a general Ω-background from which one can compute the non-perturbative gauge theory partition function using localisation. This is a non-perturbative extension of [1] and provides further evidence for our proposal of a string theory realisation of the Ω-background

  10. Anyonic Partition Functions and Windings of Planar Brownian Motion

    OpenAIRE

    Desbois, Jean; Heinemann, Christine; Ouvry, Stéphane

    1994-01-01

    The computation of the $N$-cycle brownian paths contribution $F_N(\\alpha)$ to the $N$-anyon partition function is adressed. A detailed numerical analysis based on random walk on a lattice indicates that $F_N^{(0)}(\\alpha)= \\prod_{k=1}^{N-1}(1-{N\\over k}\\alpha)$. In the paramount $3$-anyon case, one can show that $F_3(\\alpha)$ is built by linear states belonging to the bosonic, fermionic, and mixed representations of $S_3$.

  11. Ratios of partition functions for the log-gamma polymer

    OpenAIRE

    Georgiou, Nicos; Rassoul-Agha, Firas; Seppalainen, Timo; Yilmaz, Atilla

    2015-01-01

    The Annals of Probability 2015, Vol. 43, No. 5, 2282–2331 DOI: 10.1214/14-AOP933 © Institute of Mathematical Statistics, 2015 RATIOS OF PARTITION FUNCTIONS FOR THE LOG-GAMMA POLYMER BY NICOS GEORGIOU1, FIRAS RASSOUL-AGHA1, TIMO SEPPÄLÄINEN2 AND ATILLA YILMAZ3 University of Sussex, University of Utah, University of Wisconsin–Madison and Bo˘gaziçi University We introduce a random walk in random environment associated to an underlying directed polymer model in 1 ...

  12. Holographic partition functions and phases for higher genus Riemann surfaces

    Science.gov (United States)

    Maxfield, Henry; Ross, Simon F.; Way, Benson

    2016-06-01

    We describe a numerical method to compute the action of Euclidean saddle points for the partition function of a two-dimensional holographic CFT on a Riemann surface of arbitrary genus, with constant curvature metric. We explicitly evaluate the action for the saddles for genus two and map out the phase structure of dominant bulk saddles in a two-dimensional subspace of the moduli space. We discuss spontaneous breaking of discrete symmetries, and show that the handlebody bulk saddles always dominate over certain non-handlebody solutions.

  13. Holographic partition functions and phases for higher genus Riemann surfaces

    CERN Document Server

    Maxfield, Henry; Way, Benson

    2016-01-01

    We describe a numerical method to compute the action of Euclidean saddlepoints for the partition function of a two-dimensional holographic CFT on a Riemann surface of arbitrary genus, with constant curvature metric. We explicitly evaluate the action for the saddles for genus two and map out the phase structure of dominant bulk saddles in a two-dimensional subspace of the moduli space. We discuss spontaneous breaking of discrete symmetries, and show that the handlebody bulk saddles always dominate over certain non-handlebody solutions.

  14. Minimal models on Riemann surfaces: The partition functions

    Energy Technology Data Exchange (ETDEWEB)

    Foda, O. (Katholieke Univ. Nijmegen (Netherlands). Inst. voor Theoretische Fysica)

    1990-06-04

    The Coulomb gas representation of the A{sub n} series of c=1-6/(m(m+1)), m{ge}3, minimal models is extended to compact Riemann surfaces of genus g>1. An integral representation of the partition functions, for any m and g is obtained as the difference of two gaussian correlation functions of a background charge, (background charge on sphere) x (1-g), and screening charges integrated over the surface. The coupling constant x (compacitification radius){sup 2} of the gaussian expressions are, as on the torus, m(m+1), and m/(m+1). The partition functions obtained are modular invariant, have the correct conformal anomaly and - restricting the propagation of states to a single handle - one can verify explicitly the decoupling of the null states. On the other hand, they are given in terms of coupled surface integrals, and it remains to show how they degenerate consistently to those on lower-genus surfaces. In this work, this is clear only at the lattice level, where no screening charges appear. (orig.).

  15. Minimal models on Riemann surfaces: The partition functions

    International Nuclear Information System (INIS)

    The Coulomb gas representation of the An series of c=1-6/[m(m+1)], m≥3, minimal models is extended to compact Riemann surfaces of genus g>1. An integral representation of the partition functions, for any m and g is obtained as the difference of two gaussian correlation functions of a background charge, (background charge on sphere) x (1-g), and screening charges integrated over the surface. The coupling constant x (compacitification radius)2 of the gaussian expressions are, as on the torus, m(m+1), and m/(m+1). The partition functions obtained are modular invariant, have the correct conformal anomaly and - restricting the propagation of states to a single handle - one can verify explicitly the decoupling of the null states. On the other hand, they are given in terms of coupled surface integrals, and it remains to show how they degenerate consistently to those on lower-genus surfaces. In this work, this is clear only at the lattice level, where no screening charges appear. (orig.)

  16. Construction of Canonical Polynomial Basis Functions for Solving Special Nth -Order Linear Integro-Differential Equations

    Directory of Open Access Journals (Sweden)

    1 Taiwo O. A

    2013-01-01

    Full Text Available The problem of solving special nth-order linear integro-differential equations has special importance in engineering and sciences that constitutes a good model for many systems in various fields. In this paper, we construct canonical polynomial from the differential parts of special nth-order integro-differential equations and use it as our basis function for the numerical solutions of special nth-order integro-differential equations. The results obtained by this method are compared with those obtained by Adomian Decomposition method. It is also observed that the new method is an effective method with high accuracy. Some examples are given to illustrate the method.

  17. Colour-independent partition functions in coloured vertex models

    Energy Technology Data Exchange (ETDEWEB)

    Foda, O., E-mail: omar.foda@unimelb.edu.au [Dept. of Mathematics and Statistics, University of Melbourne, Parkville, VIC 3010 (Australia); Wheeler, M., E-mail: mwheeler@lpthe.jussieu.fr [Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589 (France); Université Pierre et Marie Curie – Paris 6, 4 place Jussieu, 75252 Paris cedex 05 (France)

    2013-06-11

    We study lattice configurations related to S{sub n}, the scalar product of an off-shell state and an on-shell state in rational A{sub n} integrable vertex models, n∈{1,2}. The lattice lines are colourless and oriented. The state variables are n conserved colours that flow along the line orientations, but do not necessarily cover every bond in the lattice. Choosing boundary conditions such that the positions where the colours flow into the lattice are fixed, and where they flow out are summed over, we show that the partition functions of these configurations, with these boundary conditions, are n-independent. Our results extend to trigonometric A{sub n} models, and to all n. This n-independence explains, in vertex-model terms, results from recent studies of S{sub 2} (Caetano and Vieira, 2012, [1], Wheeler, (arXiv:1204.2089), [2]). Namely, 1.S{sub 2}, which depends on two sets of Bethe roots, {b_1} and {b_2}, and cannot (as far as we know) be expressed in single determinant form, degenerates in the limit {b_1}→∞, and/or {b_2}→∞, into a product of determinants, 2. Each of the latter determinants is an A{sub 1} vertex-model partition function.

  18. Colour-independent partition functions in coloured vertex models

    International Nuclear Information System (INIS)

    We study lattice configurations related to Sn, the scalar product of an off-shell state and an on-shell state in rational An integrable vertex models, n∈{1,2}. The lattice lines are colourless and oriented. The state variables are n conserved colours that flow along the line orientations, but do not necessarily cover every bond in the lattice. Choosing boundary conditions such that the positions where the colours flow into the lattice are fixed, and where they flow out are summed over, we show that the partition functions of these configurations, with these boundary conditions, are n-independent. Our results extend to trigonometric An models, and to all n. This n-independence explains, in vertex-model terms, results from recent studies of S2 (Caetano and Vieira, 2012, [1], Wheeler, (arXiv:1204.2089), [2]). Namely, 1.S2, which depends on two sets of Bethe roots, {b1} and {b2}, and cannot (as far as we know) be expressed in single determinant form, degenerates in the limit {b1}→∞, and/or {b2}→∞, into a product of determinants, 2. Each of the latter determinants is an A1 vertex-model partition function

  19. Canonical simplicial gravity

    NARCIS (Netherlands)

    Dittrich, B.; Höhn, P.A.

    2011-01-01

    A general canonical formalism for discrete systems is developed which can handle varying phase space dimensions and constraints. The central ingredient is Hamilton's principle function which generates canonical time evolution and ensures that the canonical formalism reproduces the dynamics of the co

  20. On entire functions restricted to intervals, partition of unities, and dual Gabor frames

    DEFF Research Database (Denmark)

    Christensen, Ole; Kim, Hong Oh; Kim, Rae Young

    2014-01-01

    Partition of unities appears in many places in analysis. Typically it is generated by compactly supported functions with a certain regularity. In this paper we consider partition of unities obtained as integer-translates of entire functions restricted to finite intervals. We characterize the entire...... functions that lead to a partition of unity in this way, and we provide characterizations of the “cut-off” entire functions, considered as functions of a real variable, to have desired regularity. In particular we obtain partition of unities generated by functions with small support and desired regularity...

  1. Modular invariant partition function of critical dense polymers

    Energy Technology Data Exchange (ETDEWEB)

    Morin-Duchesne, Alexi, E-mail: a.morinduchesne@uq.edu.au [School of Mathematics and Physics, University of Queensland, St Lucia, Brisbane, Queensland 4072 (Australia); Pearce, Paul A., E-mail: p.pearce@ms.unimelb.edu.au [Department of Mathematics and Statistics, University of Melbourne, Parkville, Victoria 3010 (Australia); Rasmussen, Jørgen, E-mail: j.rasmussen@uq.edu.au [School of Mathematics and Physics, University of Queensland, St Lucia, Brisbane, Queensland 4072 (Australia)

    2013-09-01

    A lattice model of critical dense polymers is solved exactly for arbitrary system size on the torus. More generally, an infinite family of lattice loop models is studied on the torus and related to the corresponding Fortuin–Kasteleyn random cluster models. Starting with a cylinder, the commuting periodic single-row transfer matrices are built from the periodic Temperley–Lieb algebra extended by the shift operators Ω{sup ±1}. In this enlarged algebra, the non-contractible loop fugacity is α and the contractible loop fugacity is β. The torus is formed by gluing the top and bottom of the cylinder. This gives rise to a variety of non-contractible loops winding around the torus. Because of their nonlocal nature, the standard matrix trace does not produce the proper geometric torus. Instead, we introduce a modified matrix trace for this purpose. This is achieved by using a representation of the enlarged periodic Temperley–Lieb algebra with a parameter v that keeps track of the winding of defects on the cylinder. The transfer matrix representatives and their eigenvalues thus depend on v. The modified trace is constructed as a linear functional on planar connectivity diagrams in terms of matrix traces Tr{sub d} (with a fixed number of defects d) and Chebyshev polynomials of the first kind. For critical dense polymers, where β=0, the transfer matrix eigenvalues are obtained by solving a functional equation in the form of an inversion identity. The solution depends on d and is subject to selection rules which we prove. Simplifications occur if all non-contractible loop fugacities are set to α=2 in which case the traces are evaluated at v=1. In the continuum scaling limit, the corresponding conformal torus partition function obtained from finite-size corrections agrees with the known modular invariant partition function of symplectic fermions.

  2. Genus two partition and correlation functions for fermionic vertex operator superalgebras I

    OpenAIRE

    Tuite, Michael P.; Zuevsky, Alexander

    2011-01-01

    We define the partition and $n$-point correlation functions for a vertex operator superalgebra on a genus two Riemann surface formed by sewing two tori together. For the free fermion vertex operator superalgebra we obtain a closed formula for the genus two continuous orbifold partition function in terms of an infinite dimensional determinant with entries arising from torus Szeg\\"o kernels. We prove that the partition function is holomorphic in the sewing parameters on a given suitable domain ...

  3. Gauge Invariance of Resummation Schemes The QCD Partition Function

    CERN Document Server

    Achhammer, M; Leupold, S; Wiedemann, Urs Achim; Achhammer, Marc; Heinz, Ulrich; Leupold, Stefan; Wiedemann, Urs Achim

    1996-01-01

    We pick up a method originally developed by Cheng and Tsai for vacuum perturbation theory which allows to test the consistency of different sets of Feynman rules on a purely diagrammatic level, making explicit loop calculations superfluous. We generalize it to perturbative calculations in thermal field theory and we show that it can be adapted to check the gauge invariance of physical quantities calculated in improved perturbation schemes. Specifically, we extend this diagrammatic technique to a simple resummation scheme in imaginary time perturbation theory. As an application, we check up to O(g^4) in general covariant gauge the gauge invariance of the result for the QCD partition function which was recently obtained in Feynman gauge.

  4. Twists of Pl\\"ucker coordinates as dimer partition functions

    CERN Document Server

    Scott, Jeanne

    2013-01-01

    The homogeneous coordinate ring of the Grassmannian Gr(k,n) has a cluster structure defined in terms of planar diagrams known as Postnikov diagrams. The cluster corresponding to such a diagram consists entirely of Pl\\"ucker coordinates. We introduce a twist map on Gr(k,n) related to the BZ-twist, and give an explicit Laurent expansion for the twist of an arbitrary Pl\\"ucker coordinate, in terms of the cluster variables associated with a fixed Postnikov diagram. The expansion arises as a (scaled) dimer partition function of a weighted version of the bipartite graph dual to the Postnikov diagram, modified by a boundary condition determined by the Pl\\"ucker coordinate.

  5. Partition Function of 1-, 2-, and 3-D Monatomic Ideal Gas (a Simple and Comprehensive Review)

    CERN Document Server

    Khotimah, Siti Nurul

    2011-01-01

    This article discusses partition function of monatomic ideal gas which is given in Statistical Physisc at Physics Department, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia. Students in general are not familiar with partition function. This unfamiliarness was detected at a problem of partition function which was re-given in an examination in other dimensions that had been previously given in the lecture. Based on this observation, the need of a simple but comprehensive article about partition function in one-, two-, and three-dimensions is a must. For simplicity, a monatomic ideal gas is chosen.

  6. Elliptic solid-on-solid model's partition function as a single determinant

    CERN Document Server

    Galleas, W

    2016-01-01

    In this work we express the partition function of the integrable elliptic solid-on-solid model with domain-wall boundary conditions as a single determinant. This representation appears naturally as the solution of a system of functional equations governing the model's partition function.

  7. Distorted Waves with Exact Non-Local Exchange a Canonical Function Approach

    CERN Document Server

    Fakhreddine, K; Vien, G N; Tannous, C; Langlois, J M; Robaux, O

    2002-01-01

    It is shown how the Canonical Function approach can be used to obtain accurate solutions for the distorted wave problem taking account of direct static and polarisation potentials and exact non-local exchange. Calculations are made for electrons in the field of atomic hydrogen and the phaseshifts are compared with those obtained using a modified form of the DWPO code of McDowell and collaborators: for small wavenumbers our approach avoids numerical instabilities otherwise present. Comparison is also made with phaseshifts calculated using local equivalent-exchange potentials and it is found that these are inaccurate at small wavenumbers. Extension of our method to the case of atoms having other than s-type outer shells is dicussed.

  8. Smoothed analysis of partitioning algorithms for Euclidean functionals

    NARCIS (Netherlands)

    Bläser, Markus; Manthey, Bodo; Rao, B.V. Raghavendra

    2013-01-01

    Euclidean optimization problems such as TSP and minimum-length matching admit fast partitioning algorithms that compute near-optimal solutions on typical instances. In order to explain this performance, we develop a general framework for the application of smoothed analysis to partitioning algorithm

  9. Smoothed analysis of partitioning algorithms for Euclidean functionals

    NARCIS (Netherlands)

    Bläser, Markus; Manthey, Bodo; Rao, B.V. Raghavendra; Dehne, F.; Iacono, J.; Sack, J.-R.

    2011-01-01

    Euclidean optimization problems such as TSP and minimum-length matching admit fast partitioning algorithms that compute near-optimal solutions on typical instances. We develop a general framework for the application of smoothed analysis to partitioning algorithms for Euclidean optimization problems.

  10. Remarks on partition functions of topological string theory on generalized conifolds

    CERN Document Server

    Takasaki, Kanehisa

    2013-01-01

    The notion of topological vertex and the construction of topological string partition functions on local toric Calabi-Yau 3-folds are reviewed. Implications of an explicit formula of partition functions for the generalized conifolds are considered. Generating functions of part of the partition functions are shown to be tau functions of the KP hierarchy. The associated Baker-Akhiezer functions play the role of wave functions, and satisfy $q$-difference equations. These $q$-difference equations represent the quantum mirror curves conjectured by Gukov and Su{\\l}kowski.

  11. Reduced partition function ratios of iron and oxygen in goethite

    Science.gov (United States)

    Blanchard, M.; Dauphas, N.; Hu, M. Y.; Roskosz, M.; Alp, E. E.; Golden, D. C.; Sio, C. K.; Tissot, F. L. H.; Zhao, J.; Gao, L.; Morris, R. V.; Fornace, M.; Floris, A.; Lazzeri, M.; Balan, E.

    2015-02-01

    First-principles calculations based on the density functional theory (DFT) with or without the addition of a Hubbard U correction, are performed on goethite in order to determine the iron and oxygen reduced partition function ratios (β-factors). The calculated iron phonon density of states (pDOS), force constant and β-factor are compared with reevaluated experimental β-factors obtained from Nuclear Resonant Inelastic X-ray Scattering (NRIXS) measurements. The reappraisal of old experimental data is motivated by the erroneous previous interpretation of the low- and high-energy ends of the NRIXS spectrum of goethite and jarosite samples (Dauphas et al., 2012). Here the NRIXS data are analyzed using the SciPhon software that corrects for non-constant baseline. New NRIXS measurements also demonstrate the reproducibility of the results. Unlike for hematite and pyrite, a significant discrepancy remains between DFT, NRIXS and the existing Mössbauer-derived data. Calculations suggest a slight overestimation of the NRIXS signal possibly related to the baseline definition. The intrinsic features of the samples studied by NRIXS and Mössbauer spectroscopy may also contribute to the discrepancy (e.g., internal structural and/or chemical defects, microstructure, surface contribution). As for oxygen, DFT results indicate that goethite and hematite have similar β-factors, which suggests almost no fractionation between the two minerals at equilibrium.

  12. On one-loop partition functions of three-dimensional critical gravities

    NARCIS (Netherlands)

    Zojer, Thomas

    2013-01-01

    We calculate the one-loop partition function of three-dimensional parity even tricritical gravity. Agreement with logarithmic conformal field theory single-particle partition functions on the field theory side is found and we furthermore discover a partially massless limit of linearized six-derivati

  13. Relations between canonical and non-canonical inflation

    Energy Technology Data Exchange (ETDEWEB)

    Gwyn, Rhiannon [Max-Planck-Institut fuer Gravitationsphysik (Albert-Einstein-Institut), Potsdam (Germany); Rummel, Markus [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Westphal, Alexander [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Theory Group

    2012-12-15

    We look for potential observational degeneracies between canonical and non-canonical models of inflation of a single field {phi}. Non-canonical inflationary models are characterized by higher than linear powers of the standard kinetic term X in the effective Lagrangian p(X,{phi}) and arise for instance in the context of the Dirac-Born-Infeld (DBI) action in string theory. An on-shell transformation is introduced that transforms non-canonical inflationary theories to theories with a canonical kinetic term. The 2-point function observables of the original non-canonical theory and its canonical transform are found to match in the case of DBI inflation.

  14. Polymer quantization and the saddle point approximation of partition functions

    CERN Document Server

    Técotl, Hugo A Morales; Rastgoo, Saeed

    2015-01-01

    The saddle point approximation of the path integral partition functions is an important way of deriving the thermodynamical properties of black holes. However, there are certain black hole models and some mathematically analog mechanical models for which this method can not be applied directly. This is due to the fact that their action evaluated on a classical solution is not finite and its first variation does not vanish for all consistent boundary conditions. These problems can be dealt with by adding a counter-term to the classical action, which is a solution of the corresponding Hamilton-Jacobi equation. In this work we study the effects of polymer quantization on a mechanical model presenting the aforementioned difficulties and contrast it with the above counter-term method. This type of quantization for mechanical models is motivated by the loop quantization of gravity which is known to play a role in the thermodynamics of black holes systems. The model we consider is a non relativistic particle in an i...

  15. Colour-independent partition functions in coloured vertex models

    CERN Document Server

    Foda, O

    2013-01-01

    We study lattice configurations related to S_n, the scalar product of an off-shell state and an on-shell state in rational A_n integrable vertex models, n = {1, 2}. The lattice lines are colourless and oriented. The state variables are n conserved colours that flow along the line orientations, but do not necessarily cover every bond in the lattice. Choosing boundary conditions such that the positions where the colours flow into the lattice are fixed, and where they flow out are summed over, we show that the partition functions of these configurations, with these boundary conditions, are n-independent. Our results extend to trigonometric A_n models, and to all n. This n-independence explains, in vertex-model terms, results from recent studies of S_2 [1, 2]. Namely, 1. S_2 which depends on two sets of Bethe roots, b_1 and b_2, and cannot (as far as we know) be expressed in single determinant form, degenerates in the limit b_1 -> infinity, and/or b_2 -> infinity, into a product of determinants, 2. Each of the la...

  16. Genus Two Partition and Correlation Functions for Fermionic Vertex Operator Superalgebras II

    OpenAIRE

    Tuite, Michael P.; Zuevsky, Alexander

    2013-01-01

    We define and compute the continuous orbifold partition function and a generating function for all $n$-point correlation functions for the rank two free fermion vertex operator superalgebra on a genus two Riemann surface formed by self-sewing a torus. The partition function is proportional to an infinite dimensional determinant with entries arising from torus Szego kernel and the generating function is proportional to a finite determinant of genus two Szego kernels. These results follow from ...

  17. Polymer quantization and the saddle point approximation of partition functions

    Science.gov (United States)

    Morales-Técotl, Hugo A.; Orozco-Borunda, Daniel H.; Rastgoo, Saeed

    2015-11-01

    The saddle point approximation of the path integral partition functions is an important way of deriving the thermodynamical properties of black holes. However, there are certain black hole models and some mathematically analog mechanical models for which this method cannot be applied directly. This is due to the fact that their action evaluated on a classical solution is not finite and its first variation does not vanish for all consistent boundary conditions. These problems can be dealt with by adding a counterterm to the classical action, which is a solution of the corresponding Hamilton-Jacobi equation. In this work we study the effects of polymer quantization on a mechanical model presenting the aforementioned difficulties and contrast it with the above counterterm method. This type of quantization for mechanical models is motivated by the loop quantization of gravity, which is known to play a role in the thermodynamics of black hole systems. The model we consider is a nonrelativistic particle in an inverse square potential, and we analyze two polarizations of the polymer quantization in which either the position or the momentum is discrete. In the former case, Thiemann's regularization is applied to represent the inverse power potential, but we still need to incorporate the Hamilton-Jacobi counterterm, which is now modified by polymer corrections. In the latter, momentum discrete case, however, such regularization could not be implemented. Yet, remarkably, owing to the fact that the position is bounded, we do not need a Hamilton-Jacobi counterterm in order to have a well-defined saddle point approximation. Further developments and extensions are commented upon in the discussion.

  18. Computing the partition function for kinetically trapped RNA secondary structures.

    Directory of Open Access Journals (Sweden)

    William A Lorenz

    Full Text Available An RNA secondary structure is locally optimal if there is no lower energy structure that can be obtained by the addition or removal of a single base pair, where energy is defined according to the widely accepted Turner nearest neighbor model. Locally optimal structures form kinetic traps, since any evolution away from a locally optimal structure must involve energetically unfavorable folding steps. Here, we present a novel, efficient algorithm to compute the partition function over all locally optimal secondary structures of a given RNA sequence. Our software, RNAlocopt runs in O(n3 time and O(n2 space. Additionally, RNAlocopt samples a user-specified number of structures from the Boltzmann subensemble of all locally optimal structures. We apply RNAlocopt to show that (1 the number of locally optimal structures is far fewer than the total number of structures--indeed, the number of locally optimal structures approximately equal to the square root of the number of all structures, (2 the structural diversity of this subensemble may be either similar to or quite different from the structural diversity of the entire Boltzmann ensemble, a situation that depends on the type of input RNA, (3 the (modified maximum expected accuracy structure, computed by taking into account base pairing frequencies of locally optimal structures, is a more accurate prediction of the native structure than other current thermodynamics-based methods. The software RNAlocopt constitutes a technical breakthrough in our study of the folding landscape for RNA secondary structures. For the first time, locally optimal structures (kinetic traps in the Turner energy model can be rapidly generated for long RNA sequences, previously impossible with methods that involved exhaustive enumeration. Use of locally optimal structure leads to state-of-the-art secondary structure prediction, as benchmarked against methods involving the computation of minimum free energy and of maximum expected

  19. Partition and Correlation Functions of a Freely Crossed Network Using Ising Model-Type Interactions

    CERN Document Server

    Saito, Akira

    2016-01-01

    We set out to determine the partition and correlation functions of a network under the assumption that its elements are freely connected, with an Ising model-type interaction energy associated with each connection. The partition function is obtained from all combinations of loops on the free network, while the correlation function between two elements is obtained based on all combinations of routes between these points, as well as all loops on the network. These functions allow measurement of the dynamics over the whole of any network, regardless of its form. Furthermore, even as parts are added to the network, the partition and correlation functions can still be obtained. As an example, we obtain the partition and correlation functions in a crystal system under the repeated addition of fixed parts.

  20. On partition function and Weyl anomaly of conformal higher-spin fields

    International Nuclear Information System (INIS)

    We study 4-dimensional higher-derivative conformal higher-spin (CHS) fields generalizing Weyl graviton and conformal gravitino. They appear, in particular, as “induced” theories in the AdS/CFT context. We consider their partition function on curved Einstein-space backgrounds like (A)dS or sphere and Ricci-flat spaces. Remarkably, the bosonic (integer spin s) CHS partition function appears to be given by a product of partition functions of the standard 2nd-derivative “partially massless” spin s fields, generalizing the previously known expression for the 1-loop Weyl graviton (s=2) partition function. We compute the corresponding spin s Weyl anomaly coefficients as and cs. Our result for as reproduces the expression found recently in (arXiv:1306.5242) by an indirect method implied by AdS/CFT (which relates the partition function of a CHS field on S4 to a ratio of known partition functions of massless higher-spin field in AdS5 with alternate boundary conditions). We also obtain similar results for the fermionic CHS fields. In the half-integer s case the CHS partition function on (A)dS background is given by the product of squares of “partially massless” spin s partition functions and one extra factor corresponding to a special massive conformally invariant spin s field. It was noticed in (arXiv:1306.5242) that the sum of the bosonic as coefficients over all s is zero when computed using the ζ-function regularization, and we observe that the same property is true also in the fermionic case

  1. One-loop partition function of three-dimensional flat gravity

    OpenAIRE

    Barnich, Glenn; Gonzalez, Hernan A.; Maloney, Alexander; Oblak, Blagoje

    2015-01-01

    In this note we point out that the one-loop partition function of three-dimensional flat gravity, computed along the lines originally developed for the anti-de Sitter case, reproduces characters of the BMS3 group.

  2. On the domain wall partition functions of level-1 affine so(n) vertex models

    OpenAIRE

    Dow, A.; Foda, O.

    2006-01-01

    We derive determinant expressions for domain wall partition functions of level-1 affine so(n) vertex models, n >= 4, at discrete values of the crossing parameter lambda = m pi / 2(n-3), m in Z, in the critical regime.

  3. Partition function zeros at first-order phase transitions: A general analysis

    OpenAIRE

    Biskup, Marek; Borgs, Christian; Chayes, Jennifer T.; Kleinwaks, Logan J.; Kotecky, Roman

    2003-01-01

    We present a general, rigorous theory of partition function zeros for lattice spin models depending on one complex parameter. First, we formulate a set of natural assumptions which are verified for a large class of spin models in a companion paper [BBCKK2, math-ph/0304007]. Under these assumptions, we derive equations whose solutions give the location of the zeros of the partition function with periodic boundary conditions, up to an error which we prove is (generically) exponentially small in...

  4. On the analytical evaluation of the partition function for unit hypercubes in four dimensions

    International Nuclear Information System (INIS)

    The group integrations required for the analytic evaluation of the partition function for unit hypercubes in four dimensions are carried out. Modifications of the graphical rules for SU2 group integrations cited in the literature are developed for this purpose. A complete classification of all surfaces that can be embedded in the unit hypercube is given and their individual contribution to the partition function worked out. Applications are discussed briefly. (orig.)

  5. Polynomial algorithm for exact calculation of partition function for binary spin model on planar graphs

    CERN Document Server

    Karandashev, Yakov M

    2016-01-01

    In this paper we propose and realize (the code is publicly available at https://github.com/Thrawn1985/2D-Partition-Function) an algorithm for exact calculation of partition function for planar graph models with binary spins. The complexity of the algorithm is O(N^2). Test experiments shows good agreement with Onsager's analytical solution for two-dimensional Ising model of infinite size.

  6. A paradox in the electronic partition function or how to be cautious with mathematics

    Energy Technology Data Exchange (ETDEWEB)

    Miranda, E.N. [CRICYT - CONICET, Mendoza (Argentina); Departamento de Fisica, Universidad Nacional de San Luis, San Luis (Argentina)

    2001-09-01

    When the electronic partition functions of atoms or molecules are evaluated in textbooks, only the contribution of the ground state is considered. The excited states' contribution is argued to be negligible. However, a closer look shows that the partition function diverges if such states are taken into account. This paper shows that the blind use of mathematics is the reason behind this odd behaviour. (author)

  7. Wigner Distribution Functions and the Representation of Canonical Transformations in Time-Dependent Quantum Mechanics

    Directory of Open Access Journals (Sweden)

    Marcos Moshinsky

    2008-07-01

    Full Text Available For classical canonical transformations, one can, using the Wigner transformation, pass from their representation in Hilbert space to a kernel in phase space. In this paper it will be discussed how the time-dependence of the uncertainties of the corresponding time-dependent quantum problems can be incorporated into this formalism.

  8. Square-integrable solutions and Weyl functions for singular canonical systems

    NARCIS (Netherlands)

    Behrndt, Jussi; Hassi, Seppo; de Snoo, Henk; Wietsma, Rudi

    2011-01-01

    Boundary value problems for singular canonical systems of differential equations of the form Jf'(t) - H(t)f(t) = lambda Delta(t)f(t), t is an element of i, lambda is an element of C, are studied in the associated Hilbert space L(Delta)(2)(i). With the help of a monotonicity principle for matrix func

  9. Canonical field theory

    Science.gov (United States)

    You, Setthivoine

    2015-11-01

    A new canonical field theory has been developed to help interpret the interaction between plasma flows and magnetic fields. The theory augments the Lagrangian of general dynamical systems to rigourously demonstrate that canonical helicity transport is valid across single particle, kinetic and fluid regimes, on scales ranging from classical to general relativistic. The Lagrangian is augmented with two extra terms that represent the interaction between the motion of matter and electromagnetic fields. The dynamical equations can then be re-formulated as a canonical form of Maxwell's equations or a canonical form of Ohm's law valid across all non-quantum regimes. The field theory rigourously shows that helicity can be preserved in kinetic regimes and not only fluid regimes, that helicity transfer between species governs the formation of flows or magnetic fields, and that helicity changes little compared to total energy only if density gradients are shallow. The theory suggests a possible interpretation of particle energization partitioning during magnetic reconnection as canonical wave interactions. This work is supported by US DOE Grant DE-SC0010340.

  10. Computing the partition function for perfect matchings in a hypergraph

    CERN Document Server

    Barvinok, Alexander

    2010-01-01

    Given non-negative weights w_S on the k-subsets S of a km-element set V, we consider the sum of the products w_{S_1} ... w_{S_m} for all partitions V = S_1 cup ... cup S_m into pairwise disjoint k-subsets S_i. When the weights w_S are positive and within a constant factor, fixed in advance, of each other, we present a simple polynomial time algorithm to approximate the sum within a polynomial in m factor. In the process, we obtain higher-dimensional versions of the van der Waerden and Bregman-Minc bounds for permanents.

  11. Canonical quantization of macroscopic electromagnetism

    OpenAIRE

    Philbin, Thomas Gerard

    2010-01-01

    Application of the standard canonical quantization rules of quantum field theory to macroscopic electromagnetism has encountered obstacles due to material dispersion and absorption. This has led to a phenomenological approach to macroscopic quantum electrodynamics where no canonical formulation is attempted. In this paper macroscopic electromagnetism is canonically quantized. The results apply to any linear, inhomogeneous, magnetodielectric medium with dielectric functions that obey the Krame...

  12. Genus Two Partition and Correlation Functions for Fermionic Vertex Operator Superalgebras I

    CERN Document Server

    Tuite, Michael P

    2010-01-01

    We define the partition and $n$-point correlation functions for a vertex operator superalgebra on a genus two Riemann surface formed by sewing two tori together. For the free fermion vertex operator superalgebra we obtain a closed formula for the genus two continuous orbifold partition function in terms of an infinite dimensional determinant with entries arising from torus Szeg\\"o kernels. We prove that the partition function is holomorphic in the sewing parameters on a given suitable domain and describe its modular properties. Using the bosonized formalism, a new genus two Jacobi product identity is described for the Riemann theta series. We compute and discuss the modular properties of the generating function for all $n$-point functions in terms of a genus two Szeg\\"o kernel determinant. We also show that the Virasoro vector one point function satisfies a genus two Ward identity.

  13. Canonical quantization of macroscopic electromagnetism

    CERN Document Server

    Philbin, T G

    2010-01-01

    Application of the standard canonical quantization rules of quantum field theory to macroscopic electromagnetism has encountered obstacles due to material dispersion and absorption. This has led to a phenomenological approach to macroscopic quantum electrodynamics where no canonical formulation is attempted. In this paper macroscopic electromagnetism is canonically quantized. The results apply to any linear, inhomogeneous, magnetoelectric medium with dielectric functions that obey the Kramers-Kronig relations. The prescriptions of the phenomenological approach are derived from the canonical theory.

  14. Partitioning heritability by functional category using GWAS summary statistics

    DEFF Research Database (Denmark)

    Finucane, Hilary K.; Bulik-Sullivan, Brendan; Gusev, Alexander;

    2015-01-01

    in genome-wide association studies (GWAS) of 17 complex diseases and traits with an average sample size of 73,599. To enable this analysis, we introduce a new method, stratified LD score regression, for partitioning heritability from GWAS summary statistics while accounting for linked markers. This new...... method is computationally tractable at very large sample sizes and leverages genome-wide information. Our findings include a large enrichment of heritability in conserved regions across many traits, a very large immunological disease–specific enrichment of heritability in FANTOM5 enhancers and many cell...... type–specific enrichments, including significant enrichment of central nervous system cell types in the heritability of body mass index, age at menarche, educational attainment and smoking behavior....

  15. Localized operator partitioning method for electronic excitation energies in the time-dependent density functional formalism

    CERN Document Server

    Nagesh, Jayashree; Brumer, Paul; Izmaylov, Artur F

    2016-01-01

    We extend the localized operator partitioning method (LOPM) [J. Nagesh, A.F. Izmaylov, and P. Brumer, J. Chem. Phys. 142, 084114 (2015)] to the time-dependent density functional theory (TD-DFT) framework to partition molecular electronic energies of excited states in a rigorous manner. A molecular fragment is defined as a collection of atoms using Stratman-Scuseria-Frisch atomic partitioning. A numerically efficient scheme for evaluating the fragment excitation energy is derived employing a resolution of the identity to preserve standard one- and two-electron integrals in the final expressions. The utility of this partitioning approach is demonstrated by examining several excited states of two bichromophoric compounds: 9-((1-naphthyl)-methyl)-anthracene and 4-((2-naphthyl)-methyl)-benzaldehyde. The LOPM is found to provide nontrivial insights into the nature of electronic energy localization that are not accessible using simple density difference analysis.

  16. Functional Selectivity of CB2 Cannabinoid Receptor Ligands at a Canonical and Noncanonical Pathway.

    Science.gov (United States)

    Dhopeshwarkar, Amey; Mackie, Ken

    2016-08-01

    The CB2 cannabinoid receptor (CB2) remains a tantalizing, but unrealized therapeutic target. CB2 receptor ligands belong to varied structural classes and display extreme functional selectivity. Here, we have screened diverse CB2 receptor ligands at canonical (inhibition of adenylyl cyclase) and noncanonical (arrestin recruitment) pathways. The nonclassic cannabinoid (-)-cis-3-[2-hydroxy-4-(1,1-dimethylheptyl)phenyl]-trans-4-(3-hydroxypropyl)cyclohexanol (CP55940) was the most potent agonist for both pathways, while the classic cannabinoid ligand (6aR,10aR)-3-(1,1-Dimethylbutyl)-6a,7,10,10a-tetrahydro-6,6,9-trimethyl-6H-dibenzo[b,d]pyran JWH133) was the most efficacious agonist among all the ligands profiled in cyclase assays. In the cyclase assay, other classic cannabinoids showed little [(-)-trans-Δ(9)-tetrahydrocannabinol and (-)-(6aR,7,10,10aR)-tetrahydro-6,6,9-trimethyl-3-(1-methyl-1-phenylethyl)-6H-dibenzo[b,d]pyran-1-ol] (KM233) to no efficacy [(6aR,10aR)-1-methoxy-6,6,9-trimethyl-3-(2-methyloctan-2-yl)-6a,7,10,10a-tetrahydrobenzo[c]chromene(L759633) and (6aR,10aR)-3-(1,1-dimethylheptyl)-6a,7,8,9,10,10a-hexahydro-1-methoxy-6,6-dimethyl-9-methylene-6H-dibenzo[b,d]pyran]L759656. Most aminoalkylindoles, including [(3R)-​2,​3-​dihydro-​5-​methyl-​3-​(4-​morpholinylmethyl)pyrrolo[1,​2,​3-​de]-​1,​4-​benzoxazin-​6-​yl]-​1-​naphthalenyl-​methanone,​ monomethanesulfonate (WIN55212-2), were moderate efficacy agonists. The cannabilactone 3-(1,1-dimethyl-heptyl)-1-hydroxy-9-methoxy-benzo(c)chromen-6-one (AM1710) was equiefficacious to CP55940 to inhibit adenylyl cyclase, albeit with lower potency. In the arrestin recruitment assays, all classic cannabinoid ligands failed to recruit arrestins, indicating a bias toward G-protein coupling for this class of compound. All aminoalkylindoles tested, except for WIN55212-2 and (1-​pentyl-​1H-​indol-​3-​yl)(2,​2,​3,​3-​tetramethylcyclopropyl)-​methanone (UR144), failed

  17. Iterating free-field AdS/CFT: higher spin partition function relations

    Science.gov (United States)

    Beccaria, Matteo; Tseytlin, Arkady A.

    2016-07-01

    We find a simple relation between a free higher spin partition function on the thermal quotient of {{AdS}}d+1 and the partition function of the associated d-dimensional conformal higher spin field defined on the thermal quotient of {{AdS}}d. Starting with a conformal higher spin field defined in {{AdS}}d, one may also associate to with another conformal field in d-1 dimensions, thus iterating AdS/CFT. We observe that in the case of d=4, this iteration leads to a trivial 3d higher spin conformal theory with parity-even non-local action: it describes a zero total number of dynamical degrees of freedom and the corresponding partition function is equal to 1.

  18. Compactified strings as quantum statistical partition function on the Jacobian torus.

    Science.gov (United States)

    Matone, Marco; Pasti, Paolo; Shadchin, Sergey; Volpato, Roberto

    2006-12-31

    We show that the solitonic contribution of toroidally compactified strings corresponds to the quantum statistical partition function of a free particle living on higher dimensional spaces. In the simplest case of compactification on a circle, the Hamiltonian is the Laplacian on the 2g-dimensional Jacobian torus associated with the genus g Riemann surface corresponding to the string world sheet. T duality leads to a symmetry of the partition function mixing time and temperature. Such a classical-quantum correspondence and T duality shed some light on the well-known interplay between time and temperature in quantum field theory and classical statistical mechanics.

  19. Instanton partition function and two-dimensional Yang-Mills theory

    CERN Document Server

    Zhang, Xinyu

    2016-01-01

    We study four-dimensional $\\mathcal{N}=2$ supersymmetric $U(N)$ gauge theory with $2N$ fundamental hypermultiplets on the self-dual $\\Omega$-background. The partition function simplifies at special points of the parameter space, and is related to the partition function of two-dimensional Yang-Mills theory on $S^{2}$. We also consider the insertion of a Wilson loop operator in two-dimensional Yang-Mills theory, and find the corresponding operator in the four-dimensional $\\mathcal{N}=2$ gauge theory.

  20. Partition Functions for Diatomic Molecules in Plasmas out of Thermal Equilibrium

    Institute of Scientific and Technical Information of China (English)

    Geraldine FAURE

    2012-01-01

    Two calculation methods on the partition functions for diatomic molecules in plas- mas out of thermal equilibrium are reported. A Boltzmann distribution for the electronic, vi- brational and rotational quantum levels is assumed in the two calculation methods. The results obtained by two methods are displayed for four sorts of diatomic molecules, 02, N2, OH and NO, that are present in humid air plasmas. The calculation method of density for the electronically excited states is developed. Finally, a method to calculate the partition functions for simulating the non-normalized diatomic spectra is discussed.

  1. A non-canonical function of telomerase RNA in the regulation of developmental myelopoiesis in zebrafish

    Science.gov (United States)

    Alcaraz-Pérez, Francisca; García-Castillo, Jesús; García-Moreno, Diana; López-Muñoz, Azucena; Anchelin, Monique; Angosto, Diego; Zon, Leonard I.; Mulero, Victoriano; Cayuela, María L.

    2014-02-01

    Dyskeratosis congenita (DC) is an inherited disorder with mutations affecting telomerase or telomeric proteins. DC patients usually die of bone marrow failure. Here we show that genetic depletion of the telomerase RNA component (TR) in the zebrafish results in impaired myelopoiesis, despite normal development of haematopoietic stem cells (HSCs). The neutropenia caused by TR depletion is independent of telomere length and telomerase activity. Genetic analysis shows that TR modulates the myeloid-erythroid fate decision by controlling the levels of the master myeloid and erythroid transcription factors spi1 and gata1, respectively. The alteration in spi1 and gata1 levels occurs through stimulation of gcsf and mcsf. Our model of TR deficiency in the zebrafish illuminates the non-canonical roles of TR, and could establish therapeutic targets for DC.

  2. Mean Spherical Approximation-Based Partitioned Density Functional Theory

    Institute of Scientific and Technical Information of China (English)

    ZHOU Shi-Qi

    2003-01-01

    Previous literature claims that the density functional theory for non-uniform non-hard sphere interaction potential fluid can be improved on by treating the tail part by the third order functional perturbation expansion approximation (FPEA) with the symmetrical and intuitive consideration-based simple function C0(3)(r1, r2, r3) =ζ∫ dr4a(r4 - r1)a(r4 - r2)a(r4 - r3) as the uniform third order direct correlation function (DCF) for the tail part,here kernel function a(r) = (6/πσ3)Heaviside(σ/2 - r). The present contribution concludes that for the mean spherical approximation-based second order DCF, the terms higher than second order in the FPEA of the tail part of the non-uniform first order DCF are exactly zero. The reason for the partial success of the previous a kernel function-based third order FPEA for the tail part is due to the adjustable parameter ζ and the short range of the a kernel function.Improvement over the previous theories is proposed and tested.

  3. Mean Spherical Approximation-Based Partitioned Density Functional Theory

    Institute of Scientific and Technical Information of China (English)

    ZHOUShi-Qi

    2003-01-01

    Previous literature claims that the density functional theory for non-uniform non-hard sphere interaction potential fluid can be improved on by treating the tail part by the third order functional perturbation expansion approximation (FPEA) with the symmetrical and intuitive consideration-based simple function C0(3)(r1, r2, r3) =(∫dr4a(r4-r1)a(r4-r2)a(r4-r3) as the uniform third order direct correlation function (DCF) for the tail part,here kernel function a(r) = (6/πσ3)Heaviside(σ/2 - r). The present contribution concludes that for the mean spherical approximation-based second order DCF, the terms higher than second order in the FPEA of the tail part of the non-uniform first order DCF are exactly zero. The reason for the partial success of the previous a kernel function-based third order FPEA for the tail part is due to the adjustable parameter ξ and the short range of the a kernel function.Improvement over the previous theories is proposed and tested.

  4. Partitioning of minimotifs based on function with improved prediction accuracy.

    Directory of Open Access Journals (Sweden)

    Sanguthevar Rajasekaran

    Full Text Available BACKGROUND: Minimotifs are short contiguous peptide sequences in proteins that are known to have a function in at least one other protein. One of the principal limitations in minimotif prediction is that false positives limit the usefulness of this approach. As a step toward resolving this problem we have built, implemented, and tested a new data-driven algorithm that reduces false-positive predictions. METHODOLOGY/PRINCIPAL FINDINGS: Certain domains and minimotifs are known to be strongly associated with a known cellular process or molecular function. Therefore, we hypothesized that by restricting minimotif predictions to those where the minimotif containing protein and target protein have a related cellular or molecular function, the prediction is more likely to be accurate. This filter was implemented in Minimotif Miner using function annotations from the Gene Ontology. We have also combined two filters that are based on entirely different principles and this combined filter has a better predictability than the individual components. CONCLUSIONS/SIGNIFICANCE: Testing these functional filters on known and random minimotifs has revealed that they are capable of separating true motifs from false positives. In particular, for the cellular function filter, the percentage of known minimotifs that are not removed by the filter is approximately 4.6 times that of random minimotifs. For the molecular function filter this ratio is approximately 2.9. These results, together with the comparison with the published frequency score filter, strongly suggest that the new filters differentiate true motifs from random background with good confidence. A combination of the function filters and the frequency score filter performs better than these two individual filters.

  5. Drinfeld twist and the domain wall partition function of the eight-vertex model

    Institute of Scientific and Technical Information of China (English)

    Hao Kun; Chen xi; Shi Kang-Jie; Yang Wen-Li

    2011-01-01

    With the help of the F-basis provided by the Drinfeld twist or factorising F-matrix for the spatial optical soliton model associated with the eight-vertex model, we calculate the partition function for the eight-vertex model on an N × N square lattice with domain wall boundary condition.

  6. On the Definition of the Partition Function in Quantum Regge Calculus

    OpenAIRE

    Nishimura, Jun(Department, of, Particle, and, Nuclear, Physics,, Graduate, University, for, Advanced, Studies, (SOKENDAI),, Tsukuba,, Ibaraki, 305-0801,, Japan)

    1995-01-01

    We argue that the definition of the partition function used recently to demonstrate the failure of Regge calculus is wrong. In fact, in the one-dimensional case, we show that there is a more natural definition, with which one can reproduce the correct results.

  7. Optical Approach for the Thermal Partition Function of Photons

    OpenAIRE

    Moretti, Valter; Iellici, Devis

    1996-01-01

    The optical manifold method to compute the one-loop effective action in a static space-time is extended from the massless scalar field to the Maxwell field in any Feynman-like covariant gauge. The method is applied to the case of the Rindler space obtaining the same results as the point-splitting procedure. The result is free from Kabat's surface terms which instead affect the $\\zeta$-function or heat-kernel approaches working directly in the static manifold containing conical singularities. ...

  8. A Partitioned Correlation Function Interaction approach for describing electron correlation in atoms

    CERN Document Server

    Verdebout, S; Jönsson, P; Gaigalas, G; Fischer, C Froese; Godefroid, M

    2013-01-01

    Traditional multiconfiguration Hartree-Fock (MCHF) and configuration interaction (CI) methods are based on a single orthonormal orbital basis (OB). For atoms with complicated shell structures, a large OB is needed to saturate all the electron correlation effects. The large OB leads to massive configuration state function (CSF) expansions that are difficult to handle. We show that it is possible to relax the orthonormality restriction on the OB and break down the originally large calculations to a set of smaller ones that can be run in parallel. Each calculation determines a partitioned correlation function (PCF) that accounts for a specific correlation effect. The PCFs are built on optimally localized orbital sets and are added to a zero-order multireference (MR) function to form a total wave function. The mixing coefficients of the PCFs are fixed from a small generalized eigenvalue problem. The required matrices are computed using a biorthonormal transformation technique. The new method, called partitioned c...

  9. Partition functions for quantum gravity, black holes, elliptic genera and Lie algebra homologies

    Energy Technology Data Exchange (ETDEWEB)

    Bonora, L., E-mail: bonora@sissa.it [International School for Advanced Studies (SISSA), Via Bonomea 265, 34136 Trieste (Italy); INFN, Sezione di Trieste (Italy); Bytsenko, A.A., E-mail: abyts@uel.br [Departamento de Fisica, Universidade Estadual de Londrina, Caixa Postal 6001, Londrina (Brazil)

    2011-11-11

    There is a remarkable connection between quantum generating functions of field theory and formal power series associated with dimensions of chains and homologies of suitable Lie algebras. We discuss the homological aspects of this connection with its applications to partition functions of the minimal three-dimensional gravities in the space-time asymptotic to AdS{sub 3}, which also describe the three-dimensional Euclidean black holes, the pure N=1 supergravity, and a sigma model on N-fold generalized symmetric products. We also consider in the same context elliptic genera of some supersymmetric sigma models. These examples can be considered as a straightforward application of the machinery of modular forms and spectral functions (with values in the congruence subgroup of SL(2,Z)) to partition functions represented by means of formal power series that encode Lie algebra properties.

  10. Optical Approach for the Thermal Partition Function of Photons

    CERN Document Server

    Moretti, V; Moretti, Valter; Iellici, Devis

    1997-01-01

    The optical manifold method to compute the one-loop effective action in a static space-time is extended from the massless scalar field to the Maxwell field in any Feynman-like covariant gauge. The method applied in the case of the Rindler space obtaining the same results as the point-splitting procedure. The result is free from Kabat's surface terms which instead affect the manifold containing conical singularities. The relation between the optical method and the direct $\\zeta$-function approach on the Euclidean Rindler manifold is discussed both in the scalar and the photon case. Problems with the thermodynamic consistency of the results obtained from the point-splitting thermal stress tensor in the case of the Rindler space are pointed out.

  11. Covariant canonical quantization

    Energy Technology Data Exchange (ETDEWEB)

    Hippel, G.M. von [University of Regina, Department of Physics, Regina, Saskatchewan (Canada); Wohlfarth, M.N.R. [Universitaet Hamburg, Institut fuer Theoretische Physik, Hamburg (Germany)

    2006-09-15

    We present a manifestly covariant quantization procedure based on the de Donder-Weyl Hamiltonian formulation of classical field theory. This procedure agrees with conventional canonical quantization only if the parameter space is d=1 dimensional time. In d>1 quantization requires a fundamental length scale, and any bosonic field generates a spinorial wave function, leading to the purely quantum-theoretical emergence of spinors as a byproduct. We provide a probabilistic interpretation of the wave functions for the fields, and we apply the formalism to a number of simple examples. These show that covariant canonical quantization produces both the Klein-Gordon and the Dirac equation, while also predicting the existence of discrete towers of identically charged fermions with different masses. Covariant canonical quantization can thus be understood as a ''first'' or pre-quantization within the framework of conventional QFT. (orig.)

  12. Covariant canonical quantization

    CERN Document Server

    Von Hippel, G M; Hippel, Georg M. von; Wohlfarth, Mattias N.R.

    2006-01-01

    We present a manifestly covariant quantization procedure based on the de Donder-Weyl Hamiltonian formulation of classical field theory. Covariant canonical quantization agrees with conventional canonical quantization only if the parameter space is d=1 dimensional time. In d>1 quantization requires a fundamental length scale, and any bosonic field generates a spinorial wave function, leading to the purely quantum-theoretical emergence of spinors as a byproduct. We provide a probabilistic interpretation of the wave functions for the fields, and apply the formalism to a number of simple examples. These show that covariant canonical quantization produces both the Klein-Gordon and the Dirac equation, while also predicting the existence of discrete towers of identically charged fermions with different masses.

  13. Algorithm for finding partitionings of hard variants of boolean satisfiability problem with application to inversion of some cryptographic functions.

    Science.gov (United States)

    Semenov, Alexander; Zaikin, Oleg

    2016-01-01

    In this paper we propose an approach for constructing partitionings of hard variants of the Boolean satisfiability problem (SAT). Such partitionings can be used for solving corresponding SAT instances in parallel. For the same SAT instance one can construct different partitionings, each of them is a set of simplified versions of the original SAT instance. The effectiveness of an arbitrary partitioning is determined by the total time of solving of all SAT instances from it. We suggest the approach, based on the Monte Carlo method, for estimating time of processing of an arbitrary partitioning. With each partitioning we associate a point in the special finite search space. The estimation of effectiveness of the particular partitioning is the value of predictive function in the corresponding point of this space. The problem of search for an effective partitioning can be formulated as a problem of optimization of the predictive function. We use metaheuristic algorithms (simulated annealing and tabu search) to move from point to point in the search space. In our computational experiments we found partitionings for SAT instances encoding problems of inversion of some cryptographic functions. Several of these SAT instances with realistic predicted solving time were successfully solved on a computing cluster and in the volunteer computing project SAT@home. The solving time agrees well with estimations obtained by the proposed method.

  14. Algorithm for finding partitionings of hard variants of boolean satisfiability problem with application to inversion of some cryptographic functions.

    Science.gov (United States)

    Semenov, Alexander; Zaikin, Oleg

    2016-01-01

    In this paper we propose an approach for constructing partitionings of hard variants of the Boolean satisfiability problem (SAT). Such partitionings can be used for solving corresponding SAT instances in parallel. For the same SAT instance one can construct different partitionings, each of them is a set of simplified versions of the original SAT instance. The effectiveness of an arbitrary partitioning is determined by the total time of solving of all SAT instances from it. We suggest the approach, based on the Monte Carlo method, for estimating time of processing of an arbitrary partitioning. With each partitioning we associate a point in the special finite search space. The estimation of effectiveness of the particular partitioning is the value of predictive function in the corresponding point of this space. The problem of search for an effective partitioning can be formulated as a problem of optimization of the predictive function. We use metaheuristic algorithms (simulated annealing and tabu search) to move from point to point in the search space. In our computational experiments we found partitionings for SAT instances encoding problems of inversion of some cryptographic functions. Several of these SAT instances with realistic predicted solving time were successfully solved on a computing cluster and in the volunteer computing project SAT@home. The solving time agrees well with estimations obtained by the proposed method. PMID:27190753

  15. CAFFEINE: Template-Free Symbolic Model Generation of Analog Circuits via Canonical Form Functions and Genetic Programming

    CERN Document Server

    Mcconaghy, Trent; Gielen, Georges

    2011-01-01

    This paper presents a method to automatically generate compact symbolic performance models of analog circuits with no prior specification of an equation template. The approach takes SPICE simulation data as input, which enables modeling of any nonlinear circuits and circuit characteristics. Genetic programming is applied as a means of traversing the space of possible symbolic expressions. A grammar is specially designed to constrain the search to a canonical form for functions. Novel evolutionary search operators are designed to exploit the structure of the grammar. The approach generates a set of symbolic models which collectively provide a tradeoff between error and model complexity. Experimental results show that the symbolic models generated are compact and easy to understand, making this an effective method for aiding understanding in analog design. The models also demonstrate better prediction quality than posynomials.

  16. Missing Mass Approximations for the Partition Function of Stimulus Driven Ising Models

    Directory of Open Access Journals (Sweden)

    Robert eHaslinger

    2013-07-01

    Full Text Available Ising models are routinely used to quantify the second order, functional structure of neural populations. With some recent exceptions, they generally do not include the influence of time varying stimulus drive. Yet if the dynamics of network function are to be understood, time varying stimuli must be taken into account. Inclusion of stimulus drive carries a heavy computational burden because the partition function becomes stimulus dependent and must be separately calculated for all unique stimuli observed. This potentially increases computation time by the length of the data set. Here we present an extremely fast, yet simply implemented, method for approximating the stimulus dependent partition function in minutes or seconds. Noting that the most probable spike patterns (which are few occur in the training data, we sum partition function terms corresponding to those patterns explicitly. We then approximate the sum over the remaining patterns (which are improbable, but many by casting it in terms of the stimulus modulated missing mass (total stimulus dependent probability of all patterns not observed in the training data. We use use a product of conditioned logistic regression models to approximate the stimulus modulated missing mass. This method has complexity of roughly O(LNN_{pat} where is L the data length, N the number of neurons and N_{pat} the number of unique patterns in the data, contrasting with the O(L2^N complexity of alternate methods. Using multiple unit recordings from rat hippocampus, macaque DLPFC and cat Area 18 we demonstrate our method requires orders of magnitude less computation time than Monte Carlo methods and can approximate the stimulus driven partition function more accurately than either Monte Carlo methods or deterministic approximations. This advance allows stimuli to be easily included in Ising models making them suitable for studying population based stimulus encoding.

  17. Partition function of N=2* SYM on a large four-sphere

    CERN Document Server

    Hollowood, Timothy J

    2015-01-01

    We examine the partition function of N=2* supersymmetric SU(N) Yang-Mills theory on the four-sphere in the large radius limit. We point out that the large radius partition function, at fixed N, is computed by saddle points lying on particular walls of marginal stability on the Coulomb branch of the theory on R^4. For N an even (odd) integer and \\theta_YM=0, (\\pi), these include a point of maximal degeneration of the Donagi-Witten curve to a torus where BPS dyons with electric charge [N/2] become massless. We argue that the dyon singularity is the lone saddle point in the SU(2) theory, while for SU(N) with N>2, we characterize potentially competing saddle points by obtaining the relations between the Seiberg-Witten periods at such points. Using Nekrasov's instanton partition function, we solve for the maximally degenerate saddle point and obtain its free energy as a function of g_YM and N, and show that the results are "large-N exact". In the large-N theory our results provide analytical expressions for the pe...

  18. Relation between the 4d superconformal index and the S^3 partition function

    CERN Document Server

    Imamura, Yosuke

    2011-01-01

    A relation between the 4d superconformal index and the S^3 partition function is studied with focus on the 4d and 3d actions used in localization. In the case of vanishing Chern-Simons levels and round S^3 we explicitly show that the 3d action is obtained from the 4d action by dimensional reduction up to terms which do not affect the exact results. By combining this fact and a recent proposal concerning a squashing of S^3 and SU(2) Wilson line, we obtain a formula which gives the partition function depending on the Weyl weight of chiral multiplets, real mass parameters, FI parameters, and a squashing parameter as a limit of the index of a parent 4d theory.

  19. Partition functions and equilibrium constants for diatomic molecules and atoms of astrophysical interest

    CERN Document Server

    Barklem, Paul S

    2016-01-01

    Partition functions and dissociation equilibrium constants are presented for 291 diatomic molecules for temperatures in the range from near absolute zero to 10000 K, thus providing data for many diatomic molecules of astrophysical interest at low temperature. The calculations are based on molecular spectroscopic data from the book of Huber and Herzberg with significant improvements from the literature, especially updated data for ground states of many of the most important molecules by Irikura. Dissociation energies are collated from compilations of experimental and theoretical values. Partition functions for 284 species of atoms for all elements from H to U are also presented based on data collected at NIST. The calculated data are expected to be useful for modelling a range of low density astrophysical environments, especially star-forming regions, protoplanetary disks, the interstellar medium, and planetary and cool stellar atmospheres. The input data, which will be made available electronically, also prov...

  20. Unique Path Partitions

    DEFF Research Database (Denmark)

    Bessenrodt, Christine; Olsson, Jørn Børling; Sellers, James A.

    2013-01-01

    We give a complete classification of the unique path partitions and study congruence properties of the function which enumerates such partitions.......We give a complete classification of the unique path partitions and study congruence properties of the function which enumerates such partitions....

  1. Components of Intraflagellar Transport Complex A Function Independently of the Cilium to Regulate Canonical Wnt Signaling in Drosophila.

    Science.gov (United States)

    Balmer, Sophie; Dussert, Aurore; Collu, Giovanna M; Benitez, Elvira; Iomini, Carlo; Mlodzik, Marek

    2015-09-28

    The development of multicellular organisms requires the precisely coordinated regulation of an evolutionarily conserved group of signaling pathways. Temporal and spatial control of these signaling cascades is achieved through networks of regulatory proteins, segregation of pathway components in specific subcellular compartments, or both. In vertebrates, dysregulation of primary cilia function has been strongly linked to developmental signaling defects, yet it remains unclear whether cilia sequester pathway components to regulate their activation or cilia-associated proteins directly modulate developmental signaling events. To elucidate this question, we conducted an RNAi-based screen in Drosophila non-ciliated cells to test for cilium-independent loss-of-function phenotypes of ciliary proteins in developmental signaling pathways. Our results show no effect on Hedgehog signaling. In contrast, our screen identified several cilia-associated proteins as functioning in canonical Wnt signaling. Further characterization of specific components of Intraflagellar Transport complex A uncovered a cilia-independent function in potentiating Wnt signals by promoting β-catenin/Armadillo activity. PMID:26364750

  2. Towards a classification of modular invariant partition functions for theories based on N=4 superconformal algebras

    Science.gov (United States)

    Taormina, Anne

    1993-05-01

    The representation theory of the doubly extended N=4 superconformal algebra is reviewed. The modular properties of the corresponding characters can be derived, using characters sumrules for coset realizations of these N=4 algebras. Some particular combinations of massless characters are shown to transform as affine SU(2) characters under S and T, a fact used to completely classify the massless sector of the partition function.

  3. Partition functions of the Ising model on some self-similar Schreier graphs

    CERN Document Server

    D'Angeli, Daniele; Nagnibeda, Tatiana

    2010-01-01

    We study partition functions and thermodynamic limits for the Ising model on three families of finite graphs converging to infinite self-similar graphs. They are provided by three well-known groups realized as automorphism groups of regular rooted trees: the first Grigorchuk's group of intermediate growth; the iterated monodromy group of the complex polynomial $z^2-1$ known as the Basilica group; and the Hanoi Towers group $H^{(3)}$ closely related to the Sierpinsky gasket.

  4. Analysis of chromatin attachment and partitioning functions of bovine papillomavirus type 1 E2 protein.

    Science.gov (United States)

    Abroi, Aare; Ilves, Ivar; Kivi, Sirje; Ustav, Mart

    2004-02-01

    Recent studies have suggested that the tethering of viral genomes to host cell chromosomes could provide one of the ways to achieve their nuclear retention and partitioning during extrachromosomal maintenance in dividing cells. The data we present here provide firm evidence that the partitioning of the bovine papillomavirus type 1 (BPV1) genome is dependent on the chromatin attachment process mediated by viral E2 protein and its multiple binding sites. On the other hand, the attachment of E2 and the E2-mediated tethering of reporter plasmids to host chromosomes are not necessarily sufficient for efficient partitioning, suggesting that additional E2-dependent activities might be involved in the latter process. The activity of E2 protein in chromatin attachment and partitioning is more sensitive to the point mutations in the N-terminal domain than its transactivation and replication initiation functions. Therefore, at least part of the interactions of the E2 N-terminal domain with its targets during the chromatin attachment and partitioning processes are likely to involve specific receptors not involved in transactivation and replication activities of the protein. The mutational analysis also indicates that the binding of E2 to chromatin is not achieved through interaction of linear N-terminal subsequences of the E2 protein with putative receptors. Instead, the composite surface elements of the N-terminal domain build up the receptor-binding surface of E2. In this regard, the interaction of BPV1 E2 with its chromosomal targets clearly differs from the interactions of LANA1 protein from Kaposi's sarcoma-associated human herpesvirus and EBNA1 from Epstein-Barr virus with their specific receptors. PMID:14747575

  5. An efficient algorithm for upper bound on the partition function of nucleic acids.

    Science.gov (United States)

    Chitsaz, Hamidreza; Forouzmand, Elmirasadat; Haffari, Gholamreza

    2013-07-01

    It has been shown that minimum free-energy structure for RNAs and RNA-RNA interaction is often incorrect due to inaccuracies in the energy parameters and inherent limitations of the energy model. In contrast, ensemble-based quantities such as melting temperature and equilibrium concentrations can be more reliably predicted. Even structure prediction by sampling from the ensemble and clustering those structures by Sfold has proven to be more reliable than minimum free energy structure prediction. The main obstacle for ensemble-based approaches is the computational complexity of the partition function and base-pairing probabilities. For instance, the space complexity of the partition function for RNA-RNA interaction is O(n4) and the time complexity is O(n6), which is prohibitively large. Our goal in this article is to present a fast algorithm, based on sparse folding, to calculate an upper bound on the partition function. Our work is based on the recent algorithm of Hazan and Jaakkola (2012). The space complexity of our algorithm is the same as that of sparse folding algorithms, and the time complexity of our algorithm is O(MFE(n)ℓ) for single RNA and O(MFE(m, n)ℓ) for RNA-RNA interaction in practice, in which MFE is the running time of sparse folding and ℓ≤n (ℓ≤n+m) is a sequence-dependent parameter.

  6. Geometry of Spin and Spin^c structures in the M-theory partition function

    CERN Document Server

    Sati, Hisham

    2010-01-01

    We study the effects of having multiple Spin structures on the partition function of the spacetime fields in M-theory. This leads to a potential anomaly which appears in the eta-invariants upon variation of the Spin structure. The main source of such spaces are manifolds with nontrivial fundamental group, which are also important in realistic models. We extend the discussion to the Spin^c case and find the phase of the partition function, and revisit the quantization condition for the C-field in this case. In type IIA string theory in ten dimensions, the mod 2 index of the Dirac operator is the obstruction to having a well-defined partition function. We geometrically characterize manifolds with and without such an anomaly and extend to the case of nontrivial fundamental group. The lift to KO-theory gives the alpha-invariant, which in general depends on the Spin structure. This reveals many interesting connection to positive scalar curvature manifolds and constructions related to the Gromov-Lawson(-Rosenberg) ...

  7. Titchmarsh-Weyl theory for canonical systems

    Directory of Open Access Journals (Sweden)

    Keshav Raj Acharya

    2014-11-01

    Full Text Available The main purpose of this paper is to develop Titchmarsh- Weyl theory of canonical systems. To this end, we first observe the fact that Schrodinger and Jacobi equations can be written into canonical systems. We then discuss the theory of Weyl m-function for canonical systems and establish the relation between the Weyl m-functions of Schrodinger equations and that of canonical systems which involve Schrodinger equations.

  8. VizieR Online Data Catalog: Partition functions for molecules and atoms (Barklem+, 2016)

    Science.gov (United States)

    Barklem, P. S.; Collet, R.

    2016-02-01

    The results and input data are presented in the following files. Table 1 contains dissociation energies from the literature, and final adopted values, for 291 molecules. The literature values are from the compilations of Huber & Herzberg (1979, Constants of Diatomic Molecules (Van Nostrand Reinhold), Luo (2007, Comprehensive Handbook of Chemical Bond Energies (CRC Press)) and G2 theory calculations of Curtiss et al. (1991, J. Chem. Phys., 94, 7221). Table 2 contains the input data for the molecular calculations including adopted dissociation energy, nuclear spins, molecular spectroscopic constants and their sources. There are 291 files, one for each molecule, labelled by the molecule name. The various molecular spectroscopic constants are as defined in the paper. Table 4 contains the first, second and third ionisation energies for all chemical elements from H to U. The data comes from the CRC Handbook of Chemistry and Physics (Haynes, W.M. 2010, CRC Handbook of Chemistry and Physics, 91st edn. (CRC Press, Taylor and Francis Group)). Table 5a contains a list of keys to bibliographic references for the atomic energy level data that was extracted from NIST Atomic Spectra Database and used in the present work to compute atomic partition functions. The citation keys are abbreviations of the full bibliographic references which are made available in Table 5b in BibTeX format. Table 5b contains the full bibliographic references for the atomic energy level data that was extracted from the NIST Atomic Spectra Database. Table 6 contains tabulated partition function data as a function of temperature for 291 molecules. Table 7 contains tabulated equilibrium constant data as a function of temperature for 291 molecules. Table 8 contains tabulated partition function data as a function of temperature for 284 atoms and ions. The paper should be consulted for further details. (10 data files).

  9. Semiclassical partition function for strings dual to Wilson loops with small cusps in ABJM

    CERN Document Server

    Aguilera-Damia, Jeremias; Silva, Guillermo A

    2014-01-01

    We compute the 1-loop partition function for strings in $AdS_4\\times\\mathbb{CP}^3$, whose worldsheets end along a line with small cusp angles in the boundary of AdS. We obtain these 1-loop results in terms of the vacuum energy for on-shell modes. Our results verify the proposal by Lewkowycz and Maldacena in arXiv:1312.5682 for the exact Bremsstrahlung function up to the next to leading order in the strong coupling expansion. The agreement is observed for cusps distorting either the 1/2 BPS or the 1/6 BPS Wilson line.

  10. Semiclassical partition function for strings dual to Wilson loops with small cusps in ABJM

    Science.gov (United States)

    Aguilera-Damia, Jeremías; Correa, Diego H.; Silva, Guillermo A.

    2015-03-01

    We compute the 1-loop partition function for strings in , whose worldsheets end along a line with small cusp angles in the boundary of AdS. We obtain these 1-loop results in terms of the vacuum energy for on-shell modes. Our results verify the proposal by Lewkowycz and Maldacena in arXiv:1312.5682 for the exact Bremsstrahlung function up to the next to leading order in the strong coupling expansion. The agreement is observed for cusps distorting either the 1/2 BPS or the 1/6 BPS Wilson line.

  11. CaV channels and cancer: canonical functions indicate benefits of repurposed drugs as cancer therapeutics

    OpenAIRE

    Buchanan, Paul J.; McCloskey, Karen D.

    2016-01-01

    The importance of ion channels in the hallmarks of many cancers is increasingly recognised. This article reviews current knowledge of the expression of members of the voltage-gated calcium channel family (CaV) in cancer at the gene and protein level and discusses their potential functional roles. The ten members of the CaV channel family are classified according to expression of their pore-forming α-subunit; moreover, co-expression of accessory α2δ, β and γ confers a spectrum of biophysical c...

  12. A novel brain partition highlights the modular skeleton shared by structure and function.

    Science.gov (United States)

    Diez, Ibai; Bonifazi, Paolo; Escudero, Iñaki; Mateos, Beatriz; Muñoz, Miguel A; Stramaglia, Sebastiano; Cortes, Jesus M

    2015-01-01

    Elucidating the intricate relationship between brain structure and function, both in healthy and pathological conditions, is a key challenge for modern neuroscience. Recent progress in neuroimaging has helped advance our understanding of this important issue, with diffusion images providing information about structural connectivity (SC) and functional magnetic resonance imaging shedding light on resting state functional connectivity (rsFC). Here, we adopt a systems approach, relying on modular hierarchical clustering, to study together SC and rsFC datasets gathered independently from healthy human subjects. Our novel approach allows us to find a common skeleton shared by structure and function from which a new, optimal, brain partition can be extracted. We describe the emerging common structure-function modules (SFMs) in detail and compare them with commonly employed anatomical or functional parcellations. Our results underline the strong correspondence between brain structure and resting-state dynamics as well as the emerging coherent organization of the human brain.

  13. Chemical Assignment of Symmetry-Adapted Perturbation Theory Interaction Energy Components: The Functional-Group SAPT Partition.

    Science.gov (United States)

    Parrish, Robert M; Parker, Trent M; Sherrill, C David

    2014-10-14

    Recently, we introduced an effective atom-pairwise partition of the many-body symmetry-adapted perturbation theory (SAPT) interaction energy decomposition, producing a method known as atomic SAPT (A-SAPT) [Parrish, R. M.; Sherrill, C. D. J. Chem. Phys. 2014, 141, 044115]. A-SAPT provides ab initio atom-pair potentials for force field development and also automatic visualizations of the spatial contributions of noncovalent interactions, but often has difficulty producing chemically useful partitions of the electrostatic energy, due to the buildup of oscillating partial charges on adjacent functional groups. In this work, we substitute chemical functional groups in place of atoms as the relevant local quasiparticles in the partition, resulting in a functional-group-pairwise partition denoted as functional-group SAPT (F-SAPT). F-SAPT assigns integral sets of local occupied electronic orbitals and protons to chemical functional groups and linking σ bonds. Link-bond contributions can be further assigned to chemical functional groups to simplify the analysis. This approach yields a SAPT partition between pairs of functional groups with integral charge (usually neutral), preventing oscillations in the electrostatic partition. F-SAPT qualitatively matches chemical intuition and the cut-and-cap fragmentation technique but additionally yields the quantitative many-body SAPT interaction energy. The conceptual simplicity, chemical utility, and computational efficiency of F-SAPT is demonstrated in the context of phenol dimer, proflavine(+)-DNA intercalation, and a cucurbituril host-guest inclusion complex. PMID:26588139

  14. Domain wall partition function of the eight-vertex model with a non-diagonal reflecting end

    CERN Document Server

    Yang, Wen-Li; Feng, Jun; Hao, Kun; Shi, Kang-Jie; Sun, Cheng-Yi; Yang, Zhan-Ying; Zhang, Yao-Zhong

    2011-01-01

    With the help of the Drinfeld twist or factorizing F-matrix for the eight-vertex SOS model, we obtain the explicit determinant expression of the partition function of the eight-vertex model with a generic non-diagonal reflecting end and domain wall boundary condition. Our result shows that, contrary to the eight-vertex model without a reflection end, the partition function can be expressed as a single determinant.

  15. Exact partition function in $U(2)\\times U(2)$ ABJM theory deformed by mass and Fayet-Iliopoulos terms

    CERN Document Server

    Russo, Jorge G

    2015-01-01

    We exactly compute the partition function for $U(2)_k\\times U(2)_{-k}$ ABJM theory on $\\mathbb S^3$ deformed by mass $m$ and Fayet-Iliopoulos parameter $\\zeta $. For $k=1,2$, the partition function has an infinite number of Lee-Yang zeros. For general $k$, in the decompactification limit the theory exhibits a quantum (first-order) phase transition at $m=2\\zeta $.

  16. Canonical Strangeness and Distillation Effects in Hadron Production

    CERN Document Server

    Toneev, V D

    2004-01-01

    Strangeness canonical ensemble for Maxwell-Boltzmann statistics is reconsidered for excited nuclear systems with non-vanishing net strangeness. A new recurrence relation method is applied to find the partition function. The method is first generalized to the case of quantum strangeness canonical ensemble. Uncertainties in calculation of the K+/pi+ excitation function are discussed. A new scenario based on the strangeness distillation effect is put forward for a possible explanation of anomalous strangeness production observed at the bombarding energy near 30 AGeV. The peaked maximum in the K+/pi+ ratio is considered as a sign of the critical end-point reached in evolution of the system rather than a latent heat jump emerging from the onset of the first order deconfinement phase transition.

  17. Geometry of Spin and SPINc Structures in the M-Theory Partition Function

    Science.gov (United States)

    Sati, Hisham

    We study the effects of having multiple Spin structures on the partition function of the spacetime fields in M-theory. This leads to a potential anomaly which appears in the eta invariants upon variation of the Spin structure. The main sources of such spaces are manifolds with nontrivial fundamental group, which are also important in realistic models. We extend the discussion to the Spinc case and find the phase of the partition function, and revisit the quantization condition for the C-field in this case. In type IIA string theory in 10 dimensions, the (mod 2) index of the Dirac operator is the obstruction to having a well-defined partition function. We geometrically characterize manifolds with and without such an anomaly and extend to the case of nontrivial fundamental group. The lift to KO-theory gives the α-invariant, which in general depends on the Spin structure. This reveals many interesting connections to positive scalar curvature manifolds and constructions related to the Gromov-Lawson-Rosenberg conjecture. In the 12-dimensional theory bounding M-theory, we study similar geometric questions, including choices of metrics and obtaining elements of K-theory in 10 dimensions by pushforward in K-theory on the disk fiber. We interpret the latter in terms of the families index theorem for Dirac operators on the M-theory circle and disk. This involves superconnections, eta forms, and infinite-dimensional bundles, and gives elements in Deligne cohomology in lower dimensions. We illustrate our discussion with many examples throughout.

  18. Boundary superstring field theory annulus partition function in the presence of tachyons

    International Nuclear Information System (INIS)

    We compute the Boundary Superstring Field Theory partition function on the annulus in the presence of independent linear tachyon profiles on the two boundaries. The R-R sector is found to contribute non-trivially to the derivative terms of the space-time effective action. In the process we construct a boundary state description of D-branes in the presence of a linear tachyon. We quantize the open string in a tachyonic background and address the question of open/closed string duality. (author)

  19. Modular invariant partition functions for non-compact G/Ad(H) models

    CERN Document Server

    Bjornsson, Jonas

    2010-01-01

    We propose a spectrum for a class of gauged non-compact G/Ad(H) WZNW models, including spectrally flowed images of highest, lowest, and mixed extremal weight modules. These are combined into blocks whose characters, due to the Lorentzian signature of the target space, are divergent and treated as formal expressions in need of regularisation. Assuming that this is possible, we show that these extended characters transform linearly under modular transformations, and can be used to write down modular invariant partition functions.

  20. Airy Equation for the Topological String Partition Function in a Scaling Limit

    Science.gov (United States)

    Alim, Murad; Yau, Shing-Tung; Zhou, Jie

    2016-06-01

    We use the polynomial formulation of the holomorphic anomaly equations governing perturbative topological string theory to derive the free energies in a scaling limit to all orders in perturbation theory for any Calabi-Yau threefold. The partition function in this limit satisfies an Airy differential equation in a rescaled topological string coupling. One of the two solutions of this equation gives the perturbative expansion and the other solution provides geometric hints of the non-perturbative structure of topological string theory. Both solutions can be expanded naturally around strong coupling.

  1. Exact Partition Functions of Interacting Self-Avoiding Walks on Lattices

    Directory of Open Access Journals (Sweden)

    Hsieh Yu-Hsin

    2016-01-01

    Full Text Available Ideas and methods of statistical physics have been shown to be useful for understanding some interesting problems in physical systems, e.g. universality and scaling in critical systems. The interacting self-avoiding walk (ISAW on a lattice is the simplest model for homopolymers and serves as the framework of simple models for biopolymers, such as DNA, RNA, and protein, which are important components in complex systems in biology. In this paper, we briefly review our recent work on exact partition functions of ISAW. Based on zeros of these exact partition functions, we have developed a novel method in which both loci of zeros and thermodynamic functions associated with them are considered. With this method, the first zeros can be identified clearly without ambiguity. The critical point of a small system can then be defined as the peak position of the heat capacity component associated with the first zeros. For the system with two phase transitions, two pairs of first zeros corresponding to two phase transitions can be identified and overlapping Cυ can be well separated. ISAW on the simple cubic lattice is such a system where in addition to a standard collapse transition, there is another freezing transition occurring at a lower temperature. Our approach can give a clear scenario for the collapse and the freezing transitions.

  2. Partition Functions of Superconformal Chern-Simons Theories from Fermi Gas Approach

    CERN Document Server

    Moriyama, Sanefumi

    2014-01-01

    We study the partition function of three-dimensional ${\\mathcal N}=4$ superconformal Chern-Simons theories of the circular quiver type, which is a natural generalization of the ABJM theory, the worldvolume theory of M2-branes. In the ABJM case, it was known that the perturbative part of the partition function is summed up to the Airy function $e^{A}C^{-1/3}\\mathrm{Ai}[C^{-1/3}(N-B)]$ with coefficients $C$, $B$ and $A$ and for the non-perturbative part the divergences coming from the coefficients of worldsheet instantons and membrane instantons cancel among themselves. We find that many of the interesting properties in the ABJM theory are extended to the general superconformal Chern-Simons theories. Especially, we find an explicit expression of $B$ for general ${\\mathcal N}=4$ theories, a conjectural formula of $A$ for a special class, and cancellation in the non-perturbative coefficients for the next-to-simplest theory aside from the ABJM theory.

  3. Partition functions and equilibrium constants for diatomic molecules and atoms of astrophysical interest

    Science.gov (United States)

    Barklem, P. S.; Collet, R.

    2016-04-01

    Partition functions and dissociation equilibrium constants are presented for 291 diatomic molecules for temperatures in the range from near absolute zero to 10 000 K, thus providing data for many diatomic molecules of astrophysical interest at low temperature. The calculations are based on molecular spectroscopic data from the book of Huber & Herzberg (1979, Constants of Diatomic Molecules) with significant improvements from the literature, especially updated data for ground states of many of the most important molecules by Irikura (2007, J. Phys. Chem. Ref. Data, 36, 389). Dissociation energies are collated from compilations of experimental and theoretical values. Partition functions for 284 species of atoms for all elements from H to U are also presented based on data collected at NIST. The calculated data are expected to be useful for modelling a range of low density astrophysical environments, especially star-forming regions, protoplanetary disks, the interstellar medium, and planetary and cool stellar atmospheres. The input data, which will be made available electronically, also provides a possible foundation for future improvement by the community. Full Tables 1-8 are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/588/A96

  4. Thermodynamic signatures of an underlying quantum phase transition: A grand canonical approach

    Science.gov (United States)

    Jimenez, Kevin; Reslen, Jose

    2016-08-01

    The grand canonical formalism is employed to study the thermodynamic structure of a model displaying a quantum phase transition when studied with respect to the canonical formalism. A numerical survey shows that the grand partition function diverges following a power law when the interaction parameter approaches a limiting constant. The power-law exponent takes a distinctive value when such limiting constant coincides with the critical point of the subjacent quantum phase transition. An approximated expression for the grand partition function is derived analytically implementing a mean field scheme and a number of thermodynamic observables are obtained. The system observables show signatures that can be used to track the critical point of the underlying transition. This result provides a simple fact that can be exploited to verify the existence of a quantum phase transition avoiding the zero temperature regime.

  5. Thermal partition function of photons and gravitons in a Rindler wedge

    CERN Document Server

    Iellici, D; Iellici, Devis; Moretti, Valter

    1996-01-01

    The thermal partition function of photons in any covariant gauge and gravitons in the harmonic gauge, propagating in a Rindler wedge, are computed using a local zeta-function regularization approach. The correct Planckian leading order temperature dependence T^4 is obtained in both cases. For the photons, it is confirmed the existence of a surface term giving a negative contribution to the entropy, as earlier obtained by D.Kabat, but this term is shown to be gauge-dependent in the four dimensional case and therefore discarded. It is argued that similar terms could appear dealing with any integer spin s\\geq 1 in the massless case and in more general manifolds. Our conjecture is checked in the case of a graviton in the harmonic gauge, where different surface terms also appear, and physically consistent results arise dropping these terms. The results are discussed in relation to the quantum corrections to the black-hole entropy.

  6. New enumeration formulas for alternating sign matrices and square ice partition functions

    CERN Document Server

    Ayyer, Arvind

    2012-01-01

    The refined enumeration of alternating sign matrices (ASMs) of given order having prescribed behavior near one or more of their boundary edges has been the subject of extensive study, starting with the Refined Alternating Sign Matrix Conjecture of Mills-Robbins-Rumsey, its proof by Zeilberger, and more recent work on doubly-refined and triply-refined enumeration by several authors. In this paper we extend the previously known results on this problem by deriving explicit enumeration formulas for the "top-left-bottom" (triply-refined) and "top-left-bottom-right" (quadruply-refined) enumerations. The latter case solves the problem of computing the full boundary correlation function for ASMs. The enumeration formulas are proved by deriving new representations, which are of independent interest, for the partition function of the square ice model with domain wall boundary conditions at the "combinatorial point" two pi over three.

  7. The partition function of interfaces from the Nambu-Goto effective string theory

    CERN Document Server

    Billo, M; Ferro, L

    2006-01-01

    We consider the Nambu-Goto bosonic string model as a description of the physics of interfaces. By using the standard covariant quantization of the bosonic string, we derive an exact expression for the partition function in dependence of the geometry of the interface. Our expression, obtained by operatorial methods, resums the loop expansion of the NG model in the "physical gauge" computed perturbatively by functional integral methods in the literature. Recently, very accurate Monte Carlo data for the interface free energy in the 3d Ising model became avaliable. Our proposed expression compares very well to the data for values of the area sufficiently large in terms of the inverse string tension. This pattern is expected on theoretical grounds and agrees with previous analyses of other observables in the Ising model.

  8. Exact partition functions of the Ising model on MxN planar lattices with periodic-aperiodic boundary conditions

    Energy Technology Data Exchange (ETDEWEB)

    Wu, M.-C.; Hu, C.-K. [Institute of Physics, Academia Sinica, Nankang, Taipei, Taiwan (China)]. E-mails: mcwu@phys.sinica.edu.tw; huck@phys.sinica.edu.tw

    2002-06-28

    The Grassmann path integral approach is used to calculate exact partition functions of the Ising model on MxN square (sq), plane triangular (pt) and honeycomb (hc) lattices with periodic-periodic (pp), periodic-antiperiodic (pa), antiperiodic-periodic (ap) and antiperiodic-antiperiodic (aa) boundary conditions. The partition functions are used to calculate and plot the specific heat, C/k{sub B}, as a function of temperature, {theta}=k{sub B}T/J. We find that for the NxN sq lattice, C/k{sub B} for pa and ap boundary conditions are different from those for aa boundary conditions, but for the N x N pt and hc lattices, C/k{sub B} for ap, pa and aa boundary conditions have the same values. Our exact partition functions might also be useful for understanding the effects of lattice structures and boundary conditions on critical finite-size corrections of the Ising model. (author)

  9. Partition function of N=2 gauge theories on a squashed S4 with SU(2×U(1 isometry

    Directory of Open Access Journals (Sweden)

    Alejandro Cabo-Bizet

    2015-10-01

    Full Text Available We study N=2 supersymmetric gauge theories on a large family of squashed 4-spheres preserving SU(2×U(1⊂SO(4 isometry and determine the conditions under which this background is supersymmetric. We then compute the partition function of the theories by using localization technique. The results indicate that for N=2 SUSY, including both vector-multiplets and hypermultiplets, the partition function is independent of the arbitrary squashing functions as well as of the other supergravity background fields.

  10. Canonical phylogenetic ordination.

    Science.gov (United States)

    Giannini, Norberto P

    2003-10-01

    A phylogenetic comparative method is proposed for estimating historical effects on comparative data using the partitions that compose a cladogram, i.e., its monophyletic groups. Two basic matrices, Y and X, are defined in the context of an ordinary linear model. Y contains the comparative data measured over t taxa. X consists of an initial tree matrix that contains all the xj monophyletic groups (each coded separately as a binary indicator variable) of the phylogenetic tree available for those taxa. The method seeks to define the subset of groups, i.e., a reduced tree matrix, that best explains the patterns in Y. This definition is accomplished via regression or canonical ordination (depending on the dimensionality of Y) coupled with Monte Carlo permutations. It is argued here that unrestricted permutations (i.e., under an equiprobable model) are valid for testing this specific kind of groupwise hypothesis. Phylogeny is either partialled out or, more properly, incorporated into the analysis in the form of component variation. Direct extensions allow for testing ecomorphological data controlled by phylogeny in a variation partitioning approach. Currently available statistical techniques make this method applicable under most univariate/multivariate models and metrics; two-way phylogenetic effects can be estimated as well. The simplest case (univariate Y), tested with simulations, yielded acceptable type I error rates. Applications presented include examples from evolutionary ethology, ecology, and ecomorphology. Results showed that the new technique detected previously overlooked variation clearly associated with phylogeny and that many phylogenetic effects on comparative data may occur at particular groups rather than across the entire tree. PMID:14530135

  11. Calculating the partition function of N=2 Gauge theories on $S^3$ and AdS/CFT correspondence

    CERN Document Server

    Cheon, Sangmo; Kim, Nakwoo

    2011-01-01

    We test the AdS/CFT correspondence by computing the partition function of some $\\cN=2$ quiver Chern-Simons-matter theories on three-sphere. The M-theory backgrounds are of the Freund-Rubin type with the seven-dimensional internal space given as Sasaki-Einstein manifolds $Q^{1,1,1}$ or $V^{5,2}$. Localization technique reduces the exact path integral to a matrix model, and we study the large-N behavior of the partition function. For simplicity we consider only non-chiral models which have a real-valued partition function. The result is in full agreement with the prediction of the gravity duals, i.e. the free energy is proportional to $N^{3/2}$ and the coefficient matches correctly the volume of $Q^{1,1,1}$ and $V^{5,2}$.

  12. The Low Level Modular Invariant Partition Functions of Rank-Two Algebras

    CERN Document Server

    Gannon, T; Gannon, Terry

    1994-01-01

    Using the self-dual lattice method, we make a systematic search for modular invariant partition functions of the affine algebras $g\\*{(1)}$ of $g=A_2$, $A_1+A_1$, $G_2$, and $C_2$. Unlike previous computer searches, this method is necessarily complete. We succeed in finding all physical invariants for $A_2$ at levels $\\le 32$, for $G_2$ at levels $\\le 31$, for $C_2$ at levels $\\le 26$, and for $A_1+A_1$ at levels $k_1=k_2\\le 21$. This work thus completes a recent $A_2$ classification proof, where the levels $k=3,5,6,9,12,15,21$ had been left out. We also compute the dimension of the (Weyl-folded) commutant for these algebras and levels.

  13. Two-loop partition function in the planar plane-wave matrix model

    Science.gov (United States)

    Spradlin, Marcus; Van Raamsdonk, Mark; Volovich, Anastasia

    2004-12-01

    We perform two independent calculations of the two-loop partition function for the 't Hooft large N limit of the plane-wave matrix model, conjectured to be dual to the decoupled little string theory of a single spherical type IIA NS5-brane. The first is via a direct two-loop path-integral calculation in the matrix model, while the second employs the one-loop dilatation operator of four-dimensional N = 4 Yang-Mills theory truncated to the SU (2 | 4) subsector. We find precise agreement between the results of the two calculations. Various polynomials appearing in the result have rather special properties, possibly related to the large symmetry algebra of the theory or to integrability.

  14. Two-Loop Partition Function in the Planar Plane-Wave Matrix Model

    CERN Document Server

    Spradlin, M; Volovich, A; Spradlin, Marcus; Raamsdonk, Mark Van; Volovich, Anastasia

    2004-01-01

    We perform two independent calculations of the two-loop partition function for the large N 't Hooft limit of the plane-wave matrix model, conjectured to be dual to the decoupled little string theory of a single spherical type IIA NS5-brane. The first is via a direct two-loop path-integral calculation in the matrix model, while the second employs the one-loop dilatation operator of four-dimensional N = 4 Yang-Mills theory truncated to the SU(2|4) subsector. We find precise agreement between the results of the two calculations. Various polynomials appearing in the result have rather special properties, possibly related to the large symmetry algebra of the theory or to integrability.

  15. Modular invariant partition functions for the doubly extended N=4 superconformal algebras

    Energy Technology Data Exchange (ETDEWEB)

    Ooguri, Hirosi (Research Inst. for Mathematical Sciences, Kyoto Univ. (Japan) Enrico Fermi Inst., Univ. of Chicago, IL (United States)); Petersen, J.L. (Niels Bohr Inst., Copenhagen (Denmark)); Taormina, A. (Enrico Fermi Inst., Univ. of Chicago, IL (United States))

    1992-01-20

    Non-trivial modular properties of characters of the doubly extended N=4 superconformal algebras A{sub {gamma}}, A{sub {gamma}} are derived from two different points of view. First, we use realizations on Wolf spaces, in particular when one of the levels of the two commuting affine SU(2) subalgebras takes the value 2. We emphasize how these realizations involve rational torus theories, and how some specific combinations of massless characters transform under the modular group as affine SU(2) characters. Second, we show how these combinations, and generalizations thereof, emerge from a study of the explicit form of the characters when angular variables are partly restricted, but the levels are not. The two results are then combined to give stringent constraints on the modular invariant A{sub {gamma}} partition functions and they give rise to a partial classification of the latter, closely related to that of affine SU(2). (orig.).

  16. Modular invariant partition functions for the doubly extended N = 4 superconformal algebras

    Science.gov (United States)

    Ooguri, Hirosi; Petersen, Jens Lyng; Taormina, Anne

    1992-01-01

    Non-trivial modular properties of characters of the doubly extended N = 4 superconformal algebras Aγ, Ãγ are derived from two different points of view. First, we use realizations on Wolf spaces, in particular when one of the levels of the two commuting affine SU(2) subalgebras takes the value 2. We emphasize how these realizations involve rational torus theories, and how some specific combinations of massless characters transform under the modular group as affine SU(2) characters. Second, we show how these combinations, and generalizations thereof, emerge from a study of the explicit form of the characters when angular variables are partly restricted, but the levels are not. The two results are then combined to give stringent constraints on the modular invariant Ãγ partition functions and they give rise to a partial classification of the latter, closely related to that of affine SU(2).

  17. The star-triangle relation, lens partition function, and hypergeometric sum/integrals

    CERN Document Server

    Gahramanov, Ilmar

    2016-01-01

    The aim of the present paper is to consider the hyperbolic limit of an elliptic hypergeometric sum/integral identity, and associated lattice model of statistical mechanics previously obtained by the second author. The hyperbolic sum/integral identity obtained from this limit, has two important physical applications in the context of the so-called gauge/YBE correspondence. For statistical mechanics, this identity is equivalent to a new solution of the star-triangle relation form of the Yang-Baxter equation, that directly generalises the Faddeev-Volkov models to the case of discrete and continuous spin variables. On the gauge theory side, this identity represents the duality of lens ($S_b^3/\\mathbb{Z}_r$) partition functions, for certain three-dimensional $\\mathcal N = 2$ supersymmetric gauge theories.

  18. Revisiting Interpretation of Canonical Correlation Analysis: A Tutorial and Demonstration of Canonical Commonality Analysis

    Science.gov (United States)

    Nimon, Kim; Henson, Robin K.; Gates, Michael S.

    2010-01-01

    In the face of multicollinearity, researchers face challenges interpreting canonical correlation analysis (CCA) results. Although standardized function and structure coefficients provide insight into the canonical variates produced, they fall short when researchers want to fully report canonical effects. This article revisits the interpretation of…

  19. Spin glass: thermal properties and characterization of the ± J Sherrington-Kirkpatrick model partition function zeros

    International Nuclear Information System (INIS)

    A detailed study of the S-K model through the analysis of the zeros of the partition function in the complex temperature plane is performed. By the exact way, the notable thermodynamical properties of the system to a variety of the length (N=5→25 spins) are calculated, using only standards concepts (without the use of tricks like that of replicas). Dilute models had been also considered. The principal result of this work is the characterization of the zeros of the partition function of the S-K model. (author)

  20. The Homotopic Probability Distribution and the Partition Function for the Entangled System Around a Ribbon Segment Chain

    Institute of Scientific and Technical Information of China (English)

    QIAN Shang-Wu; GU Zhi-Yu

    2001-01-01

    Using the Feynman's path integral with topological constraints arising from the presence of one singular line, we find the homotopic probability distribution PnL for the winding number n and the partition function PL of the entangled system around a ribbon segment chain. We find that when the width of the ribbon segment chain 2a increases,the partition function exponentially decreases, whereas the free energy increases an amount, which is proportional to the square of the width. When the width tends to zero we obtain the same results as those of a single chain with one singular point.

  1. Canonical density matrix perturbation theory.

    Science.gov (United States)

    Niklasson, Anders M N; Cawkwell, M J; Rubensson, Emanuel H; Rudberg, Elias

    2015-12-01

    Density matrix perturbation theory [Niklasson and Challacombe, Phys. Rev. Lett. 92, 193001 (2004)] is generalized to canonical (NVT) free-energy ensembles in tight-binding, Hartree-Fock, or Kohn-Sham density-functional theory. The canonical density matrix perturbation theory can be used to calculate temperature-dependent response properties from the coupled perturbed self-consistent field equations as in density-functional perturbation theory. The method is well suited to take advantage of sparse matrix algebra to achieve linear scaling complexity in the computational cost as a function of system size for sufficiently large nonmetallic materials and metals at high temperatures. PMID:26764847

  2. Neutrophil elastase (NE) and NE inhibitors: canonical and noncanonical functions in lung chronic inflammatory diseases (cystic fibrosis and chronic obstructive pulmonary disease).

    Science.gov (United States)

    Roghanian, Ali; Sallenave, Jean-Michel

    2008-03-01

    Proteases and antiproteases have multiple important roles both in normal homeostasis and during inflammation. Antiprotease molecules may have developed in a parallel network, consisting of "alarm" and "systemic" inhibitors. Their primary function was thought until recently to mainly prevent the potential injurious effects of excess release of proteolytic enzymes, such as neutrophil elastase (NE), from inflammatory cells. However, recently, new potential roles have been ascribed to these antiproteases. We will review "canonical" and new "noncanonical" functions for these molecules, and more particularly, those pertaining to their role in innate and adaptive immunity (antibacterial activity and biasing of the adaptive immune response). PMID:18518838

  3. A phyletic perspective on the allometry of plant biomass-partitioning patterns and functionally equivalent organ-categories.

    Science.gov (United States)

    Niklas, Karl J

    2006-01-01

    Biomass-partitioning patterns influence the functioning of aquatic and terrestrial vegetation at all levels, ranging from individual growth and reproduction to the flow of mass and energy through entire communities. For this reason, leaf, stem and root dry biomass-partitioning patterns across taxonomically and ecologically diverse seed plants (spermatophytes) have been intensively investigated, both empirically and theoretically. By contrast, phyletically disparate plants (e.g. green and brown algal macrophytes, mosses and pteridophytes) have not been examined to determine whether the partitioning of their body parts into 'leaf', 'stem' and 'root' analogs accords with that of spermatophytes. In this review, the biomass-partitioning patterns of siphonous and brown algal macrophytes, mosses and pteridophytes were compared allometrically with those of spermatophytes and were shown to be largely in statistical accordance (thus lending support to the hypothesis that a single scaling relationship exists across eukaryotic photoautotrophs). This concordance is argued to support the hypothesis of functional equivalence across analogous, but developmentally different, body parts, a feature that permits the use of simpler biological model systems with which to derive analytical explanations for the biomass-partitioning patterns reported for more complex seed plants.

  4. Transfer functions for solid solution partitioning of cadmium for Australian soils

    NARCIS (Netherlands)

    Vries, de W.; Mc Laughlin, M.J.; Groenenberg, J.E.

    2011-01-01

    To assess transport and ecotoxicological risks of metals, such as cadmium (Cd) in soils, models are needed for partitioning and speciation. We derived regression-based “partition-relations” based on adsorption and desorption experiments for main Australian soil types. First, batch adsorption experim

  5. Hierarchical partitioning of metazoan protein conservation profiles provides new functional insights.

    Directory of Open Access Journals (Sweden)

    Jonathan Witztum

    Full Text Available The availability of many complete, annotated proteomes enables the systematic study of the relationships between protein conservation and functionality. We explore this question based solely on the presence or absence of protein homologues (a.k.a. conservation profiles. We study 18 metazoans, from two distinct points of view: the human's and the fly's. Using the GOrilla gene ontology (GO analysis tool, we explore functional enrichment of the "universal proteins", those with homologues in all 17 other species, and of the "non-universal proteins". A large number of GO terms are strongly enriched in both human and fly universal proteins. Most of these functions are known to be essential. A smaller number of GO terms, exhibiting markedly different properties, are enriched in both human and fly non-universal proteins. We further explore the non-universal proteins, whose conservation profiles are consistent with the "tree of life" (TOL consistent, as well as the TOL inconsistent proteins. Finally, we applied Quantum Clustering to the conservation profiles of the TOL consistent proteins. Each cluster is strongly associated with one or a small number of specific monophyletic clades in the tree of life. The proteins in many of these clusters exhibit strong functional enrichment associated with the "life style" of the related clades. Most previous approaches for studying function and conservation are "bottom up", studying protein families one by one, and separately assessing the conservation of each. By way of contrast, our approach is "top down". We globally partition the set of all proteins hierarchically, as described above, and then identify protein families enriched within different subdivisions. While supporting previous findings, our approach also provides a tool for discovering novel relations between protein conservation profiles, functionality, and evolutionary history as represented by the tree of life.

  6. Hierarchical partitioning of metazoan protein conservation profiles provides new functional insights.

    Science.gov (United States)

    Witztum, Jonathan; Persi, Erez; Horn, David; Pasmanik-Chor, Metsada; Chor, Benny

    2014-01-01

    The availability of many complete, annotated proteomes enables the systematic study of the relationships between protein conservation and functionality. We explore this question based solely on the presence or absence of protein homologues (a.k.a. conservation profiles). We study 18 metazoans, from two distinct points of view: the human's and the fly's. Using the GOrilla gene ontology (GO) analysis tool, we explore functional enrichment of the "universal proteins", those with homologues in all 17 other species, and of the "non-universal proteins". A large number of GO terms are strongly enriched in both human and fly universal proteins. Most of these functions are known to be essential. A smaller number of GO terms, exhibiting markedly different properties, are enriched in both human and fly non-universal proteins. We further explore the non-universal proteins, whose conservation profiles are consistent with the "tree of life" (TOL consistent), as well as the TOL inconsistent proteins. Finally, we applied Quantum Clustering to the conservation profiles of the TOL consistent proteins. Each cluster is strongly associated with one or a small number of specific monophyletic clades in the tree of life. The proteins in many of these clusters exhibit strong functional enrichment associated with the "life style" of the related clades. Most previous approaches for studying function and conservation are "bottom up", studying protein families one by one, and separately assessing the conservation of each. By way of contrast, our approach is "top down". We globally partition the set of all proteins hierarchically, as described above, and then identify protein families enriched within different subdivisions. While supporting previous findings, our approach also provides a tool for discovering novel relations between protein conservation profiles, functionality, and evolutionary history as represented by the tree of life. PMID:24594619

  7. Pattern-Driven Architectural Partitioning. Balancing Functional and Non-functional Requirements

    NARCIS (Netherlands)

    Harrison, Neil; Avgeriou, Paris

    2007-01-01

    One of the vexing challenges of software architecture is the problem of satisfying the functional specifications of the system to be created while at the same time meeting its non-functional needs. In this work we focus on the early stages of the software architecture process, when initial high-leve

  8. Partition function on spheres: how (not) to use zeta function regularization

    CERN Document Server

    Monin, A

    2016-01-01

    It is known that not all summation methods are linear and stable. Zeta function regularization is in general non-linear. However, in some cases formal manipulations with "zeta function" regularization (assuming linearity of sums) lead to correct results. We consider several examples and show why this happens.

  9. Reverse energy partitioning—An efficient algorithm for computing the density of states, partition functions, and free energy of solids

    Science.gov (United States)

    Do, Hainam; Wheatley, Richard J.

    2016-08-01

    A robust and model free Monte Carlo simulation method is proposed to address the challenge in computing the classical density of states and partition function of solids. Starting from the minimum configurational energy, the algorithm partitions the entire energy range in the increasing energy direction ("upward") into subdivisions whose integrated density of states is known. When combined with the density of states computed from the "downward" energy partitioning approach [H. Do, J. D. Hirst, and R. J. Wheatley, J. Chem. Phys. 135, 174105 (2011)], the equilibrium thermodynamic properties can be evaluated at any temperature and in any phase. The method is illustrated in the context of the Lennard-Jones system and can readily be extended to other molecular systems and clusters for which the structures are known.

  10. Exact partition functions for the $\\Omega$-deformed $\\mathcal N=2^{*}$ $SU(2)$ gauge theory

    CERN Document Server

    Beccaria, Matteo

    2016-01-01

    We study the low energy effective action of the $\\Omega$-deformed $\\mathcal N =2^{*}$ $SU(2) $ gauge theory. It depends on the deformation parameters $\\epsilon_{1},\\epsilon_{2}$, the scalar field expectation value $a$, and the hypermultiplet mass $m$. We explore the plane $(\\frac{m}{\\epsilon_{1}}, \\frac{\\epsilon_{2}}{\\epsilon_{1}})$ looking for special features in the multi-instanton contributions to the prepotential, motivated by what happens in the Nekrasov-Shatashvili limit $\\epsilon_{2}\\to 0$. We propose a simple condition on the structure of poles of the $k$-instanton prepotential and show that it is admissible at a finite set of points in the above plane. At these special points, the prepotential has poles at fixed positions independent on the instanton number. Besides and remarkably, both the instanton partition function and the full prepotential, including the perturbative contribution, may be given in closed form as functions of the scalar expectation value $a$ and the modular parameter $q$ appearing...

  11. Influence of pressure derivative of partition function on thermodynamic properties of non-local thermodynamic equilibrium thermal plasma

    Science.gov (United States)

    Singh, Gurpreet; Sharma, Rohit; Singh, Kuldip

    2015-09-01

    Thermodynamic properties (compressibility coefficient Z γ , specific heat at constant volume c v , adiabatic coefficient γ a , isentropic coefficient γ i s e n , and sound speed c s ) of non-local thermodynamic equilibrium hydrogen thermal plasma have been investigated for different values of pressure and non-equilibrium parameter θ (=Te/Th) in the electron temperature range from 6000 K to 60 000 K. In order to estimate the influence of pressure derivative of partition function on thermodynamic properties, two cases have been considered: (a) in which pressure derivative of partition function is taken into account in the expressions and (b) without pressure derivative of partition function in their expressions. Here, the case (b) represents expressions already available in literature. It has been observed that the temperature from which pressure derivative of partition function starts influencing a given thermodynamic property increases with increase of pressure and non-equilibrium parameter θ. Thermodynamic property in the case (a) is always greater than its value in the case (b) for compressibility coefficient and specific heat at constant volume, whereas for adiabatic coefficient, isentropic coefficient, and sound speed, its value in the case (a) is always less than its value in the case (b). For a given value of θ, the relationship of compressibility coefficient with degree of ionization depends upon pressure in the case (a), whereas it is independent of pressure in the case (b). Relative deviation between the two cases shows that the influence of pressure derivative of partition function is significantly large and increases with the augmentation of pressure and θ for compressibility coefficient, specific heat at constant volume, and adiabatic coefficient, whereas for isentropic coefficient and sound speed, it is marginal even at high values of pressure and non-equilibrium parameter θ.

  12. Multiplicity fluctuations in heavy-ion collisions using canonical and grand-canonical ensemble

    Energy Technology Data Exchange (ETDEWEB)

    Garg, P. [Indian Institute of Technology Indore, Discipline of Physics, School of Basic Science, Simrol (India); Mishra, D.K.; Netrakanti, P.K.; Mohanty, A.K. [Bhabha Atomic Research Center, Nuclear Physics Division, Mumbai (India)

    2016-02-15

    We report the higher-order cumulants and their ratios for baryon, charge and strangeness multiplicity in canonical and grand-canonical ensembles in ideal thermal model including all the resonances. When the number of conserved quanta is small, an explicit treatment of these conserved charges is required, which leads to a canonical description of the system and the fluctuations are significantly different from the grand-canonical ensemble. Cumulant ratios of total-charge and net-charge multiplicity as a function of collision energies are also compared in grand-canonical ensemble. (orig.)

  13. Analysis of Chromatin Attachment and Partitioning Functions of Bovine Papillomavirus Type 1 E2 Protein

    OpenAIRE

    Abroi, Aare; Ilves, Ivar; Kivi, Sirje; Ustav, Mart

    2004-01-01

    Recent studies have suggested that the tethering of viral genomes to host cell chromosomes could provide one of the ways to achieve their nuclear retention and partitioning during extrachromosomal maintenance in dividing cells. The data we present here provide firm evidence that the partitioning of the bovine papillomavirus type 1 (BPV1) genome is dependent on the chromatin attachment process mediated by viral E2 protein and its multiple binding sites. On the other hand, the attachment of E2 ...

  14. The perturbative partition function of supersymmetric 5D Yang-Mills theory with matter on the five-sphere

    CERN Document Server

    Kallen, Johan; Zabzine, Maxim

    2012-01-01

    Based on the construction by Hosomichi, Seong and Terashima we consider N=1 supersymmetric 5D Yang-Mills theory with matter on a five-sphere with radius r. This theory can be thought of as a deformation of the theory in flat space with deformation parameter r and this deformation preserves 8 supercharges. We calculate the full perturbative partition function as a function of r/g^2, where g is the Yang-Mills coupling, and the answer is given in terms of a matrix model. We perform the calculation using localization techniques. We also argue that in the large N-limit of this deformed 5D Yang-Mills theory this matrix model provides the leading contribution to the partition function and the rest is exponentially suppressed.

  15. Experimental determination of Pb partitioning between sulfide melt and basalt melt as a function of P, T and X

    Science.gov (United States)

    Hart, Stanley R.; Gaetani, Glenn A.

    2016-07-01

    We have measured the partition coefficient of Pb (KdPb) between FeS melt and basalt melt at temperatures of 1250-1523 °C, pressures of 1.0-3.5 GPa and oxygen fugacities at iron-wustite and wustite-magnetite. The total observed range of KdPb is 4.0-66.6, with a strong negative dependence on pressure and a strong negative dependence on FeO of the silicate melt (Fe+2 only). The FeO control was constrained over a wide range of FeO (4.2-39.5%). We found that the effect of oxygen fugacity can be subsumed under the FeO control parameter. Prior work has established the lack of a significant effect of temperature (Kiseeva and Wood, 2015; Li and Audétat, 2015). Our data are parameterized as: KdPb = 4.8 + (512 - 119*P in GPa)*(1/FeO - 0.021). We also measured a single value of KdPb between clinopyroxene and basalt melt at 2.0 GPa of 0.020 ± 0.001. This experimental data supports the "natural" partitioning of Pb measured on sulfide globules in MORB (Patten et al., 2013), but not the low KdPb of ∼3 inferred from sulfides in abyssal peridotites by Warren and Shirey (2012). It also quantitatively affirms the modeling of Hart and Gaetani (2006) with respect to using sulfide to buffer the canonical Nd/Pb ratio for MORB and OIB (Hofmann, 2003). For the low FeO and pressure of segregation typical of MORB, KdPb ∼ 45, and the Nd/Pb ratio of erupted basalts will be the same as the Nd/Pb ratio of the mantle source. The remaining puzzle is why MORB and OIB have the same Nd/Pb when they clearly have different FeO and pressure of melt segregation.

  16. A whole-path importance-sampling scheme for Feynman path integral calculations of absolute partition functions and free energies.

    Science.gov (United States)

    Mielke, Steven L; Truhlar, Donald G

    2016-01-21

    Using Feynman path integrals, a molecular partition function can be written as a double integral with the inner integral involving all closed paths centered at a given molecular configuration, and the outer integral involving all possible molecular configurations. In previous work employing Monte Carlo methods to evaluate such partition functions, we presented schemes for importance sampling and stratification in the molecular configurations that constitute the path centroids, but we relied on free-particle paths for sampling the path integrals. At low temperatures, the path sampling is expensive because the paths can travel far from the centroid configuration. We now present a scheme for importance sampling of whole Feynman paths based on harmonic information from an instantaneous normal mode calculation at the centroid configuration, which we refer to as harmonically guided whole-path importance sampling (WPIS). We obtain paths conforming to our chosen importance function by rejection sampling from a distribution of free-particle paths. Sample calculations on CH4 demonstrate that at a temperature of 200 K, about 99.9% of the free-particle paths can be rejected without integration, and at 300 K, about 98% can be rejected. We also show that it is typically possible to reduce the overhead associated with the WPIS scheme by sampling the paths using a significantly lower-order path discretization than that which is needed to converge the partition function. PMID:26801023

  17. A whole-path importance-sampling scheme for Feynman path integral calculations of absolute partition functions and free energies.

    Science.gov (United States)

    Mielke, Steven L; Truhlar, Donald G

    2016-01-21

    Using Feynman path integrals, a molecular partition function can be written as a double integral with the inner integral involving all closed paths centered at a given molecular configuration, and the outer integral involving all possible molecular configurations. In previous work employing Monte Carlo methods to evaluate such partition functions, we presented schemes for importance sampling and stratification in the molecular configurations that constitute the path centroids, but we relied on free-particle paths for sampling the path integrals. At low temperatures, the path sampling is expensive because the paths can travel far from the centroid configuration. We now present a scheme for importance sampling of whole Feynman paths based on harmonic information from an instantaneous normal mode calculation at the centroid configuration, which we refer to as harmonically guided whole-path importance sampling (WPIS). We obtain paths conforming to our chosen importance function by rejection sampling from a distribution of free-particle paths. Sample calculations on CH4 demonstrate that at a temperature of 200 K, about 99.9% of the free-particle paths can be rejected without integration, and at 300 K, about 98% can be rejected. We also show that it is typically possible to reduce the overhead associated with the WPIS scheme by sampling the paths using a significantly lower-order path discretization than that which is needed to converge the partition function.

  18. Experimental Energy Levels and Partition Function of the 12C2 Molecule

    Science.gov (United States)

    Furtenbacher, Tibor; Szabó, István; Császár, Attila G.; Bernath, Peter F.; Yurchenko, Sergei N.; Tennyson, Jonathan

    2016-06-01

    The carbon dimer, the 12C2 molecule, is ubiquitous in astronomical environments. Experimental-quality rovibronic energy levels are reported for 12C2, based on rovibronic transitions measured for and among its singlet, triplet, and quintet electronic states, reported in 42 publications. The determination utilizes the Measured Active Rotational-Vibrational Energy Levels (MARVEL) technique. The 23,343 transitions measured experimentally and validated within this study determine 5699 rovibronic energy levels, 1325, 4309, and 65 levels for the singlet, triplet, and quintet states investigated, respectively. The MARVEL analysis provides rovibronic energies for six singlet, six triplet, and two quintet electronic states. For example, the lowest measurable energy level of the {{a}}{}3{{{\\Pi }}}{{u}} state, corresponding to the J = 2 total angular momentum quantum number and the F 1 spin-multiplet component, is 603.817(5) cm‑1. This well-determined energy difference should facilitate observations of singlet–triplet intercombination lines, which are thought to occur in the interstellar medium and comets. The large number of highly accurate and clearly labeled transitions that can be derived by combining MARVEL energy levels with computed temperature-dependent intensities should help a number of astrophysical observations as well as corresponding laboratory measurements. The experimental rovibronic energy levels, augmented, where needed, with ab initio variational ones based on empirically adjusted and spin–orbit coupled potential energy curves obtained using the Duo code, are used to obtain a highly accurate partition function, and related thermodynamic data, for 12C2 up to 4000 K.

  19. TREE SPECIES COMMUNITY SPATIAL PARTITION IN FUNCTION OF SOIL DRAINAGE IN AN ARAUCARIA FOREST FRAGMENT IN SOUTHERN BRAZIL

    OpenAIRE

    Pedro Higuchi; Ana Carolina da Silva; Manoela Drews de Aguiar; Álvaro Luiz Mafra; Marcelo Negrini; Diego Fernando Zech

    2014-01-01

    http://dx.doi.org/10.5902/1980509814580The relationship vegetation-soil can contribute to understand the forest structure, supporting biodiversity conservation. Thus, the aim of the present study was to verify the existence of spatial partition of the tree species community in an Araucaria forest fragment in function of soil drainage. For this sake, an environmental characterization (soil drainage, physical and chemical soil properties, topography, compression of soil, depth of soil and canop...

  20. On Partition of Unities Generated by Entire Functions and Gabor Frames in L2(Rd) and ℓ2(Zd)

    DEFF Research Database (Denmark)

    Christensen, Ole; Kim, Hong Oh; Kim, Rae Young

    2016-01-01

    We characterize the entire functions P of d variables, d≥2, for which the Zd-translates of Pχ[0,N]d satisfy the partition of unity for some N∈N. In contrast to the one-dimensional case, these entire functions are not necessarily periodic. In the case where P is a trigonometric polynomial, we...... characterize the maximal smoothness of Pχ[0,N]d, as well as the function that achieves it. A number of especially attractive constructions are achieved, e.g., of trigonometric polynomials leading to any desired (finite) regularity for a fixed support size. As an application we obtain easy constructions...

  1. The Partition of Unity Method for High-Order Finite Volume Schemes Using Radial Basis Functions Reconstruction

    Institute of Scientific and Technical Information of China (English)

    Serena Morigi; Fiorella Sgallari

    2009-01-01

    This paper introduces the use of partition of unity method for the develop-ment of a high order finite volume discretization scheme on unstructured grids for solv-ing diffusion models based on partial differential equations. The unknown function and its gradient can be accurately reconstructed using high order optimal recovery based on radial basis functions. The methodology proposed is applied to the noise removal prob-lem in functional surfaces and images. Numerical results demonstrate the effectiveness of the new numerical approach and provide experimental order of convergence.

  2. Process modelling on a canonical basis[Process modelling; Canonical modelling

    Energy Technology Data Exchange (ETDEWEB)

    Siepmann, Volker

    2006-12-20

    possible to retrieve symbolically obtained derivatives of arbitrary process properties with respect to process parameters efficiently as a post calculation. The approach is therefore perfectly suitable to perform advanced process systems engineering tasks, such as sensitivity analysis, process optimisation, and data reconciliation. The concept of canonical modelling yields a natural definition of a general exergy state function for second law analysis. By partitioning of exergy into latent, mechanical, and chemical contributions, irreversible effects can be identified specifically, even for black-box models. The calculation core of a new process simulator called Yasim is developed and implemented. The software design follows the concepts described in the theoretical part of this thesis. Numerous exemplary process models are presented to address various subtopics of canonical modelling (author)

  3. On partitions avoiding right crossings

    OpenAIRE

    Yan, Sherry H. F.; Xu, Yuexiao

    2011-01-01

    Recently, Chen et al. derived the generating function for partitions avoiding right nestings and posed the problem of finding the generating function for partitions avoiding right crossings. In this paper, we derive the generating function for partitions avoiding right crossings via an intermediate structure of partial matchings avoiding 2-right crossings and right nestings. We show that there is a bijection between partial matchings avoiding 2-right crossing and right nestings and partitions...

  4. Marine microalgae growth and carbon partitioning as a function of nutrient availability.

    Science.gov (United States)

    Fernandes, Tomásia; Fernandes, Igor; Andrade, Carlos A P; Cordeiro, Nereida

    2016-08-01

    To understand in which way the structural differences of three marine microalgae (Nannochloropsis gaditana, Rhodomonas marina and Isochrysis sp.) affect their carbon partitioning, growth and applicability; a stoichiometric imbalance was imposed by steady carbon and other nutrients variation. Towards high nutrients concentrations/low carbon availability a decrease of 12-51% in C/N microalgae ratio was observed and maximum cell densities were achieved. Moreover, linear correlation between the nutrient input and microalgae protein content were observed. The macromolecular ratios pointed that carbohydrate was the main contributor for the C/N decrement. Although lipid content in R. marina remained constant throughout the experiment, a rise of 37-107% in N. gaditana and Isochrysis sp. was verified. Lipid fractions revealed high percentages of glycolipids in all microalgae (57-73% of total lipids). The present study shows an easy way to understand and modulate microalgae carbon partitioning relying on the field of application. PMID:27179298

  5. Concerted action of plasmid maintenance functions: partition complexes create a requirement for dimer resolution.

    Science.gov (United States)

    Bouet, Jean-Yves; Bouvier, Marie; Lane, David

    2006-12-01

    Partition of prokaryotic DNA requires formation of specific protein-centromere complexes, but an excess of the protein can disrupt segregation. The mechanisms underlying this destabilization are unknown. We have found that destabilization by the F plasmid partition protein, SopB, of plasmids carrying the F centromere, sopC, results from the capacity of the SopB-sopC partition complex to stimulate plasmid multimerization. Mutant SopBs unable to destabilize failed to increase multimerization. Stability of wild-type mini-F, whose ResD/rfsF site-specific recombination system enables it to resolve multimers to monomers, was barely affected by excess SopB. Destabilization of plasmids lacking the rfsF site was suppressed by recF, recO and recR, but not by recB, mutant alleles, indicating that multimerization is initiated from single-strand gaps. SopB did not alter the amounts or distribution of replication intermediates, implying that SopB-DNA complexes do not create single-strand gaps by blocking replication forks. Rather, the results are consistent with SopB-DNA complexes channelling gapped molecules into the RecFOR recombination pathway. We suggest that extended SopB-DNA complexes increase the likelihood of recombination between sibling plasmids by keeping them in close contact prior to SopA-mediated segregation. These results cast plasmid site-specific resolution in a new role - compensation for untoward consequences of partition complex formation. PMID:17059567

  6. Canonical Information Analysis

    DEFF Research Database (Denmark)

    Vestergaard, Jacob Schack; Nielsen, Allan Aasbjerg

    2015-01-01

    Canonical correlation analysis is an established multivariate statistical method in which correlation between linear combinations of multivariate sets of variables is maximized. In canonical information analysis introduced here, linear correlation as a measure of association between variables...... is replaced by the information theoretical, entropy based measure mutual information, which is a much more general measure of association. We make canonical information analysis feasible for large sample problems, including for example multispectral images, due to the use of a fast kernel density estimator...... for entropy estimation. Canonical information analysis is applied successfully to (1) simple simulated data to illustrate the basic idea and evaluate performance, (2) fusion of weather radar and optical geostationary satellite data in a situation with heavy precipitation, and (3) change detection in optical...

  7. Classifying Linear Canonical Relations

    OpenAIRE

    Lorand, Jonathan

    2015-01-01

    In this Master's thesis, we consider the problem of classifying, up to conjugation by linear symplectomorphisms, linear canonical relations (lagrangian correspondences) from a finite-dimensional symplectic vector space to itself. We give an elementary introduction to the theory of linear canonical relations and present partial results toward the classification problem. This exposition should be accessible to undergraduate students with a basic familiarity with linear algebra.

  8. Partition functions of 3d $\\hat D$-quivers and their mirror duals from 1d free fermions

    CERN Document Server

    Assel, Benjamin; Felix, Jan

    2015-01-01

    We study the matrix models calculating the sphere partition functions of 3d gauge theories with $\\mathcal{N}=4$ supersymmetry and a quiver structure of a $\\hat D$ Dynkin diagram (where each node is a unitary gauge group). As in the case of necklace ($\\hat A $) quivers, we can map the problem to that of free fermion quantum mechanics whose complicated Hamiltonian we find explicitly. Many of these theories are conjectured to be dual under mirror symmetry to certain unitary linear quivers with extra Sp nodes or antisymmetric hypermultiplets. We show that the free fermion formulations of such mirror pairs are related by a linear symplectic transformation. We then study the large N expansion of the partition function, which as in the case of the $\\hat A$-quivers is given to all orders in 1/N by an Airy function. We simplify the algorithm to calculate the numerical coefficients appearing in the Airy function and evaluate them for a wide class of $\\hat D$-quiver theories.

  9. [Canon Busting and Cultural Literacy.

    Science.gov (United States)

    National Forum: Phi Kappa Phi Journal, 1989

    1989-01-01

    Articles on literary canon include: "Educational Anomie" (Stephen W. White); "Why Western Civilization?" (William J. Bennett); "Peace Plan for Canon Wars" (Gerald Graff, William E. Cain); "Canons, Cultural Literacy, and Core Curriculum" (Lynne V. Cheney); "Canon Busting: Basic Issues" (Stanley Fish); "A Truce in Curricular Wars" (Chester E. Finn,…

  10. Density Functional Theory and Grand Canonical Monte Carlo Simulations of the Hydrogen Storage Properties of Partially Truncated and Open Cage C60 Fullerenes

    Institute of Scientific and Technical Information of China (English)

    LI Xiao-Dong; TANG Yong-Jian; CHENG Xin-Lu; ZHANG Hong

    2011-01-01

    The potential energies of H2 molecules with partially truncated and open cage C6o fullerenes,including Css,C55,C54(Ⅰ),C54(Ⅱ) and C46,are investigated by means of the density functional theory method.The energy barrier for one H2 molecule (with two postures) entering into the nanocage decreases from 435.59 (513.45)kcal/mol to 3.64 (-2.06) kcal/mol with the increase of the truncated pore.The grand canonical Monte Carlo simulations reveal that each nanocage can accommodate only one H2 molecule inside its cavity at both 77K and 298K.All the other H2 molecules are adsorbed round the truncated pores outside the nanocages.Exceptionally,the truncated C46 can store 2.28wt% H2 molecules at 77K.Therefore,the truncating part of the C60 molecule may be a novel idea to explore C60 fullerene as a hydrogen storage material.Hydrogen is one of the clean and renewable energy carriers used to replace traditional fossil fuels,which have caused great negative effects on the environment.However,the main obstacle for the wide use of hydrogen is its dense and safe storage.[1-3] One proposed method is to physisorbe molecular hydrogen on porous materials.[4-6] Some studies found that metal organic frameworks have the potential to satisfy the goal of gravimetric density of 6wt% hydrogen,[6-9]as set by the U.S.Department of Energy in 2010.However,it is unfortunate that the synthesis of these artificially designed frames is a tremendous obstacle.%The potential energies of H2 molecules with partially truncated and open cage C60 fullerenes, including C58, C55, C54(I), C54(I) and C46, are investigated by means of the density functional theory method. The energy barrier for one H2 molecule (with two postures) entering into the nanocage decreases from 435.59 (513.45) kcal/mol to 3.64 (-2.06) kcal/mol with the increase of the truncated pore. The grand canonical Monte Carlo simulations reveal that each nanocage can accommodate only one H2 molecule inside its cavity at both 77 K and 298 K. All

  11. Evaluation of brain functional states based on projections of electroencephalographic spectral parameters on 2-dimensional canonical space.

    Science.gov (United States)

    Won, Seung-Hee; Jang, Hwan-Soo; Lee, Ho-Won; Jang, Il-Sung; Lee, Maan-Gee

    2012-10-15

    Electroencephalographic (EEG) activities reflect the functional state of the brain, but it is difficult to objectively describe functional brain states. Here, we describe two statistical divergence measures, Mahalanobis distance and Hellinger distance of projections to the reference spaces, to evaluate their state-discriminating ability. Last, divergence measures of 30-min segments after caffeine treatment were compared to evaluate the dose- and time-dependent arousal effects of caffeine to the best reference space. EEG was recorded from Sprague-Dawley rats during pre- and post-administration of caffeine. Several two-dimensional reference spaces were constructed from subsets of the normalized 7 relative band powers pooled from the pre-drug period of all recordings for each cortex: two reference spaces from data sets of the frontal and parietal cortex, and four reference spaces from data sets of active wake, slow-wave sleep, paradoxical sleep state, and all states. Sleep-wake states used as test states were plotted onto the reference spaces, and then, two divergence measures were derived to measure state-discriminating ability of each reference space. First, the reference space of the same cortex as test data was better for discriminating test states than another cortical reference space. Second, the one reference space constructed from data of all states was better for discriminating test states than the other reference spaces. Third, divergence measures were well correlated with sleep-wake durations after caffeine administration and showed the temporal trends of caffeine-induced arousal effect. These results suggest that two statistical measures can objectively describe brain functional states and drug-induced states.

  12. Canonical transfer-function realization for Schur multipliers on the Drury-Arveson space and models for commuting row contractions

    CERN Document Server

    Ball, Joseph A

    2011-01-01

    We develop a $d$-variable analog of the two-component de Bran-ges-Rovnyak reproducing kernel Hilbert space associated with a Schur-class function on the unit disk. In this generalization, the unit disk is replaced by the unit ball in $d$-dimensional complex Euclidean space, and the Schur class becomes the class of contractive multipliers on the Drury-Arveson space over the ball. We also develop some results on a model theory for commutative row contractions which are not necessarily completely noncoisometric (the case considered in earlier work of Bhattacharyya, Eschmeier and Sarkar)

  13. Gene Duplication of the zebrafish kit ligand and partitioning of melanocyte development functions to kit ligand a.

    Directory of Open Access Journals (Sweden)

    Keith A Hultman

    2007-01-01

    Full Text Available The retention of particular genes after the whole genome duplication in zebrafish has given insights into how genes may evolve through partitioning of ancestral functions. We examine the partitioning of expression patterns and functions of two zebrafish kit ligands, kit ligand a (kitla and kit ligand b (kitlb, and discuss their possible coevolution with the duplicated zebrafish kit receptors (kita and kitb. In situ hybridizations show that kitla mRNA is expressed in the trunk adjacent to the notochord in the middle of each somite during stages of melanocyte migration and later expressed in the skin, when the receptor is required for melanocyte survival. kitla is also expressed in other regions complementary to kita receptor expression, including the pineal gland, tail bud, and ear. In contrast, kitlb mRNA is expressed in brain ventricles, ear, and cardinal vein plexus, in regions generally not complementary to either zebrafish kit receptor ortholog. However, like kitla, kitlb is expressed in the skin during stages consistent with melanocyte survival. Thus, it appears that kita and kitla have maintained congruent expression patterns, while kitb and kitlb have evolved divergent expression patterns. We demonstrate the interaction of kita and kitla by morpholino knockdown analysis. kitla morphants, but not kitlb morphants, phenocopy the null allele of kita, with defects for both melanocyte migration and survival. Furthermore, kitla morpholino, but not kitlb morpholino, interacts genetically with a sensitized allele of kita, confirming that kitla is the functional ligand to kita. Last, we examine kitla overexpression in embryos, which results in hyperpigmentation caused by an increase in the number and size of melanocytes. This hyperpigmentation is dependent on kita function. We conclude that following genome duplication, kita and kitla have maintained their receptor-ligand relationship, coevolved complementary expression patterns, and that

  14. Variation in functional rooting depth and soil water partitioning along an elevational gradient in the southwestern U.S

    Science.gov (United States)

    Guo, J.; Hungate, B. A.; Kolb, T.; KOCH, G. W.

    2012-12-01

    In semi-arid environments, co-existing plant species may vary in rooting depth, reflecting functional differences in water sources. In mountains of the southwestern U.S., moisture availability increases with elevation and winter and summer precipitation inputs differ isotopically. Examining variation in functional rooting depth among different plant communities and seasons is important to understanding how these communities may respond to the predicted warming and drying of the Southwest. The goal of this study was to assess the water partitioning of the woody plant community along an elevational moisture gradient using water isotopes as a proxy for rooting depth. We hypothesized that spatial and temporal water partitioning would be greatest in low elevation, moisture-stressed sites and would decrease as moisture availability increases with elevation. Five plots were established in each of five biotic communities: upland Sonoran desert, pinyon-juniper woodland, ponderosa pine forest, mixed-conifer forest, and spruce-fir forest. Soils (surface, 20 cm, 40 cm) and stem samples of dominant woody perennials were sampled during the late spring dry season and in late summer following monsoon rains, water was extracted using a cryo-vacuum line, and δD and δ18O values were determined by off-axis cavity ringdown spectroscopy. Soil moisture content increased with elevation across all sites and increased with soil depth in the desert, pinyon-juniper, and ponderosa sites. The δD values differed significantly among species in the desert and the ponderosa forest communities (p=0.014 and 0.039 ), while no species differences in δD were found in the pinyon-juniper woodland or mixed-conifer forest. With the exception of the pinyon-juniper woodland, these data support our hypothesis that niche differentiation between species becomes less significant higher on the topographic moisture gradient, in the mixed-conifer forest. While spatial water partitioning mostly follows our

  15. Extended Function of Plasmid Partition Genes: the Sop System of Linear Phage-Plasmid N15 Facilitates Late Gene Expression▿

    Science.gov (United States)

    Ravin, Nikolai V.; Rech, Jérôme; Lane, David

    2008-01-01

    The mitotic stability of the linear plasmid-prophage N15 of Escherichia coli depends on a partition system closely related to that of the F plasmid SopABC. The two Sop systems are distinguished mainly by the arrangement of their centromeric SopB-binding sites, clustered in F (sopC) and dispersed in N15 (IR1 to IR4). Because two of the N15 inverted repeat (IR) sites are located close to elements presumed (by analogy with phage λ) to regulate late gene expression during the lytic growth of N15, we asked whether Sop partition functions play a role in this process. In N15, a putative Q antiterminator gene is located 6 kb upstream of the probable major late promoter and two intrinsic terminator-like sequences, in contrast to λ, where the Q gene is adjacent to the late promoter. Northern hybridization and lacZ reporter activity confirmed the identity of the N15 late promoter (p52), demonstrated antiterminator activity of the Q analogue, and located terminator sequences between p52 and the first open reading frame. Following prophage induction, N15 mutated in IR2 (downstream from gene Q) or IR3 (upstream of p52) showed a pronounced delay in lysis relative to that for wild-type N15. Expression of ir3−-p52::lacZ during N15 wild-type lytic growth was strongly reduced relative to the equivalent ir3+ fusion. The provision of Q protein and the IR2 and SopAB proteins in trans to ir3+-p52::lacZ increased expression beyond that seen in the absence of any one of these factors. These results indicate that the N15 Sop system has a dual role: partition and regulation of late gene transcription during lytic growth. PMID:18359814

  16. Climate change and water use partitioning by different plant functional groups in a grassland on the Tibetan Plateau.

    Directory of Open Access Journals (Sweden)

    Jia Hu

    Full Text Available The Tibetan Plateau (TP is predicted to experience increases in air temperature, increases in snowfall, and decreases in monsoon rains; however, there is currently a paucity of data that examine the ecological responses to such climate changes. In this study, we examined the effects of increased air temperature and snowfall on: 1 water use partitioning by different plant functional groups, and 2 ecosystem CO2 fluxes throughout the growing season. At the individual plant scale, we used stable hydrogen isotopes (δD to partition water use between shallow- and deep-rooted species. Prior to the arrival of summer precipitation (typically mid-July, snowmelt was the main water source in the soils. During this time, shallow and deep-rooted species partitioned water use by accessing water from shallow and deep soils, respectively. However, once the monsoon rains arrived, all plants used rainwater from the upper soils as the main water source. Snow addition did not result in increased snowmelt use throughout the growing season; instead, snowmelt water was pushed down into deeper soils when the rains arrived. At the larger plot scale, CO2 flux measurements demonstrated that rain was the main driver for net ecosystem productivity (NEP. NEP rates were low during June and July and reached a maximum during the monsoon season in August. Warming decreased NEP through a reduction in gross primary productivity (GPP, and snow additions did not mitigate the negative effects of warming by increasing NEP or GPP. Both the isotope and CO2 flux results suggest that rain drives productivity in the Nam Tso region on the TP. This also suggests that the effects of warming-induced drought on the TP may not be mitigated by increased snowfall. Further decreases in summer monsoon rains may affect ecosystem productivity, with large implications for livestock-based livelihoods.

  17. Canonical affordances in context

    Directory of Open Access Journals (Sweden)

    Alan Costall

    2012-12-01

    Full Text Available James Gibson’s concept of affordances was an attempt to undermine the traditional dualism of the objective and subjective. Gibson himself insisted on the continuity of “affordances in general” and those attached to human artifacts. However, a crucial distinction needs to be drawn between “affordances in general” and the “canonical affordances” that are connected primarily to artifacts. Canonical affordances are conventional and normative. It is only in such cases that it makes sense to talk of the affordance of the object. Chairs, for example, are for sitting-on, even though we may also use them in many other ways. A good deal of confusion has arisen in the discussion of affordances from (1 the failure to recognize the normative status of canonical affordances and (2 then generalizing from this special case.

  18. On the Relativistic Micro-Canonical Ensemble and Relativistic Kinetic Theory for N Relativistic Particles in Inertial and Non-Inertial Rest Frames

    OpenAIRE

    Alba, David; Crater, Horace W.; Lusanna, Luca

    2012-01-01

    A new formulation of relativistic classical mechanics allows a revisiting of old unsolved problems in relativistic kinetic theory and in relativistic statistical mechanics. In particular a definition of the relativistic micro-canonical partition function is given strictly in terms of the Poincar\\'e generators of an interacting N-particle system both in the inertial and non-inertial rest frames. The non-relativistic limit allows a definition of both the inertial and non-inertial micro-canonica...

  19. Fixed conditions for achieving the real-valued partition function of one-dimensional Gross-Pitaevskii equation coupled with time-dependent potential

    Energy Technology Data Exchange (ETDEWEB)

    Prayitno, T. B., E-mail: trunk-002@unj.ac.id [Physics Department, Faculty of Mathematics and Natural Science, Universitas Negeri Jakarta, Jl. Pemuda Rawamangun no. 10, Jakarta, 13220 (Indonesia)

    2014-03-24

    We have imposed the conditions in order to preserve the real-valued partition function in the case of onedimensional Gross-Pitaevskii equation coupled by time-dependent potential. In this case we have solved the Gross-Pitaevskii equation by means of the time-dependent perturbation theory by extending the previous work of Kivshar et al. [Phys. Lett A 278, 225–230 (2001)]. To use the method, we have treated the equation as the macroscopic quantum oscillator and found that the expression of the partition function explicitly has complex values. In fact, we have to choose not only the appropriate functions but also the suitable several values of the potential to keep the real-valued partition function.

  20. Metal-Silicate Partitioning of Bi, In, and Cd as a Function of Temperature and Melt Composition

    Science.gov (United States)

    Marin, Nicole; Righter, K.; Danielson, L.; Pando, K.; Lee, C.

    2013-01-01

    The origin of volatile elements in the Earth, Moon and Mars is not known; however, several theories have been proposed based on volatile elements such as In, As, Se, Te and Zn which are in lower concentration in the Earth, Moon, and Mars than in chondrites. Explanations for these low concentrations are based on two contrasting theories for the origin of Earth: equilibrium core formation versus late accretion. One idea is that the volatiles were added during growth of the planets and Moon, and some mobilized into the metallic core while others stayed in the mantle (e.g., [1]). The competing idea is that they were added to the mantles after core formation had completed (e.g., [2]). Testing these ideas involves quantitative modeling which can only be performed after data is obtained on the systematic metal-silicate partitioning behavior of volatile elements with temperature, pressure and melt composition. Until now, such data for Bi, In, and Cd has been lacking. After conducting a series of high pressure, high temperature experiments, the metal-silicate partition coefficients of Bi, In, and Cd as a function of temperature and melt composition can be used to evaluate potential conditions under which terrestrial planets differentiated into core and mantle, and how they acquired volatiles.

  1. TREE SPECIES COMMUNITY SPATIAL PARTITION IN FUNCTION OF SOIL DRAINAGE IN AN ARAUCARIA FOREST FRAGMENT IN SOUTHERN BRAZIL

    Directory of Open Access Journals (Sweden)

    Pedro Higuchi

    2014-06-01

    Full Text Available http://dx.doi.org/10.5902/1980509814580The relationship vegetation-soil can contribute to understand the forest structure, supporting biodiversity conservation. Thus, the aim of the present study was to verify the existence of spatial partition of the tree species community in an Araucaria forest fragment in function of soil drainage. For this sake, an environmental characterization (soil drainage, physical and chemical soil properties, topography, compression of soil, depth of soil and canopy cover was realized in 25 plots of 20 x 20m, where tree individuals, with circumference at breast height ≥15.7 cm were previously counted, measured and identified. The data were analysed by Mann-Withney test, non-parametric multivariate ANOVA (NPMANOVA, multivariate analysis (NMDS and indicator species analysis. In this small spatial scale there were two drainage classes, corresponding to well and moderately-drained soils, with environmental differences that determined the richness, the spatial partition of the tree community and the occurrence of indicator species. Thus, we conclude that in the study forest fragment soil drainage spatial variations were determinant in the floristic-structural heterogeneity observed in tree community. 

  2. On Partitions of Goldbach's Conjecture

    OpenAIRE

    Woon, Max S. C.

    2000-01-01

    An approximate formula for the partitions of Goldbach's Conjecture is derived using Prime Number Theorem and a heuristic probabilistic approach. A strong form of Goldbach's conjecture follows in the form of a lower bounding function for the partitions of Goldbach's conjecture. Numerical computations suggest that the lower and upper bounding functions for the partitions satisfy a simple functional equation. Assuming that this invariant scaling property holds for all even integer $n$, the lower...

  3. The canonical and grand canonical models for nuclear multifragmentation

    Indian Academy of Sciences (India)

    G Chaudhuri; S Das Gupta

    2010-08-01

    Many observables seen in intermediate energy heavy-ion collisions can be explained on the basis of statistical equilibrium. Calculations based on statistical equilibrium can be implemented in microcanonical ensemble, canonical ensemble or grand canonical ensemble. This paper deals with calculations with canonical and grand canonical ensembles. A recursive relation developed recently allows calculations with arbitrary precision for many nuclear problems. Calculations are done to study the nature of phase transition in nuclear matter.

  4. A theorem concerning twisted and untwisted partition functions in U(N) and SU(N) lattice gauge theories

    International Nuclear Information System (INIS)

    In order to get a clue to understanding the volume-dependence of vortex free energy (which is defined as the ratio of the twisted against the untwisted partition function), we investigate the relation between vortex free energies defined on lattices of different sizes. An equality is derived through a simple calculation which equates a general linear combination of vortex free energies defined on a lattice to that on a smaller lattice. The couplings in the denominator and in the numerator however shows a discrepancy, and we argue that it vanishes in the thermodynamic limit. Comparison between our result and the work of Tomboulis is also presented. In the appendix we carefully examine the proof of quark confinement by Tomboulis and summarize its loopholes

  5. Calculations of reduced partition function ratios of hydrated boric acid molecule by the ab initio molecular orbital theory

    International Nuclear Information System (INIS)

    Based on the ab initio molecular orbital theory at the HF/6-31G(d) level, the effect of hydration on the reduced partition function ratio (RPFR) of the boric acid molecule (B(OH)3) was evaluated in order to better understand boron isotope fractionation observed in aqueous systems. The B(OH)3(H2O)n species with n up to 12 were considered and their geometry optimization and RPFR calculations were carried out. It was induced that hydration decreased the RPFR of B(OH)3 and the degree of decrease in ln(RPFR) was ca. 1.5%, which was nearly equivalent to that of B(OH)4-. (author)

  6. Vitamin B6 nutritional status and cellular availability of pyridoxal 5'-phosphate govern the function of the transsulfuration pathway's canonical reactions and hydrogen sulfide production via side reactions.

    Science.gov (United States)

    Gregory, Jesse F; DeRatt, Barbara N; Rios-Avila, Luisa; Ralat, Maria; Stacpoole, Peter W

    2016-07-01

    The transsulfuration pathway (TS) acts in sulfur amino acid metabolism by contributing to the regulation of cellular homocysteine, cysteine production, and the generation of H2S for signaling functions. Regulation of TS pathway kinetics involves stimulation of cystathionine β-synthase (CBS) by S-adenosylmethionine (SAM) and oxidants such as H2O2, and by Michaelis-Menten principles whereby substrate concentrations affect reaction rates. Although pyridoxal phosphate (PLP) serves as coenzyme for both CBS and cystathionine γ-lyase (CSE), CSE exhibits much greater loss of activity than CBS during PLP insufficiency. Thus, cellular and plasma cystathionine concentrations increase in vitamin B6 deficiency mainly due to the bottleneck caused by reduced CSE activity. Because of the increase in cystathionine, the canonical production of cysteine (homocysteine → cystathionine → cysteine) is largely maintained even during vitamin B6 deficiency. Typical whole body transsulfuration flux in humans is 3-7 μmol/h per kg body weight. The in vivo kinetics of H2S production via side reactions of CBS and CSE in humans are unknown but they have been reported for cultured HepG2 cells. In these studies, cells exhibit a pronounced reduction in H2S production capacity and rates of lanthionine and homolanthionine synthesis in deficiency. In humans, plasma concentrations of lanthionine and homolanthionine exhibit little or no mean change due to 4-wk vitamin B6 restriction, nor do they respond to pyridoxine supplementation of subjects in chronically low-vitamin B6 status. Wide individual variation in responses of the H2S biomarkers to such perturbations of human vitamin B6 status suggests that the resulting modulation of H2S production may have physiological consequences in a subset of people. Supported by NIH grant DK072398. This paper refers to data from studies registered at clinicaltrials.gov as NCT01128244 and NCT00877812. PMID:26765812

  7. Realizations of the Canonical Representation

    Indian Academy of Sciences (India)

    M K Vemuri

    2008-02-01

    A characterisation of the maximal abelian subalgebras of the bounded operators on Hilbert space that are normalised by the canonical representation of the Heisenberg group is given. This is used to classify the perfect realizations of the canonical representation.

  8. Rhythmic canons and modular tiling

    OpenAIRE

    Caure, Hélianthe

    2016-01-01

    This thesis is a contribution to the study of modulo p tiling. Many mathematical and computational tools were used for the study of rhythmic tiling canons. Recent research has mainly focused in finding tiling without inner periodicity, being called Vuza canons. Those canons are a constructive basis for all rhythmic tiling canons, however, they are really difficult to obtain. Best current method is a brut force exploration that, despite a few recent enhancements, is exponential. Many technics ...

  9. On using enriched cover function in the Partition-of-unity method for singular boundary-value problems

    Science.gov (United States)

    Liu, X.; Lee, C. K.; Fan, S. C.

    Amongst the various approaches of `meshless' method, the Partition-of-unity concept married with the traditional finite-element method, namely PUFEM, has emerged to be competitive in solving the boundary-value problems. It inherits most of the advantages from both techniques except that the beauty of being `meshless' vanishes. This paper presents an alternative approach to solve singular boundary-value problems. It follows the basic PUFEM procedures. The salient feature is to enhance the quality of the influence functions, either over one single nodal cover or multi-nodal-covers. In the vicinity of the singularity, available asymptotic analytical solution is employed to enrich the influence function. The beauty of present approach is that it facilitates easy replacement of the influence functions. In other words, it favors the `influence-function refinement' procedure in a bid to search for more accurate solutions. It is analogous to the `p-version refinement' in the traditional finite-element procedures. The present approach can yield very accurate solution without adopting refined meshes. As a result, the quantities around the singularity can be evaluated directly once the nodal values are solved. No additional post-processing is needed. Firstly, the formulation of the present PUFEM approach is described. Subsequently, illustrative examples show the application to three classical singular benchmark problems having various orders of singularity. Results obtained through mesh refinements, single-nodal-cover refinements or multi-nodal-cover refinements are compared.

  10. A Network Partition Algorithm for Mining Gene Functional Modules of Colon Cancer from DNA Microarray Data

    Institute of Scientific and Technical Information of China (English)

    Xiao-Gang Ruan; Jin-Lian Wang; Jian-Geng Li

    2006-01-01

    Computational analysis is essential for transforming the masses of microarray data into a mechanistic understanding of cancer. Here we present a method for finding gene functional modules of cancer from microarray data and have applied it to colon cancer. First, a colon cancer gene network and a normal colon tissue gene network were constructed using correlations between the genes. Then the modules that tended to have a homogeneous functional composition were identified by splitting up the network. Analysis of both networks revealed that they are scale-free.Comparison of the gene functional modules for colon cancer and normal tissues showed that the modules' functions changed with their structures.

  11. q-series, elliptic curves, and odd values of the partition function

    OpenAIRE

    Nicholas Eriksson

    1999-01-01

    Let p(n) be the number of partitions of an integer n. Euler proved the following recurrence for p(n): p(n)=∑k=1∞(−1)k+1(p(n−É(k))+p(n−É(−k))),                                        (*) where É(k)=(3k 2+k)/2. In view of Euler's result, one sees that it is ...

  12. Canonical Strangeness Enhancement

    CERN Document Server

    Sollfrank, J; Redlich, Krzysztof; Satz, Helmut

    1998-01-01

    According to recent experimental data and theoretical developments we discuss three distinct topics related to strangeness enhancement in nuclear reactions. We investigate the compatibility of multi-strange particle ratios measured in a restricted phase space with thermal model parameters extracted recently in 4pi. We study the canonical suppression as a possible reason for the observed strangeness enhancement and argue that a connection between QGP formation and the undersaturation of strangeness is not excluded.

  13. Resource partitioning along multiple niche axes drives functional diversity in parrotfishes on Caribbean coral reefs.

    Science.gov (United States)

    Adam, Thomas C; Kelley, Megan; Ruttenberg, Benjamin I; Burkepile, Deron E

    2015-12-01

    The recent loss of key consumers to exploitation and habitat degradation has significantly altered community dynamics and ecosystem function across many ecosystems worldwide. Predicting the impacts of consumer losses requires knowing the level of functional diversity that exists within a consumer assemblage. In this study, we document functional diversity among nine species of parrotfishes on Caribbean coral reefs. Parrotfishes are key herbivores that facilitate the maintenance and recovery of coral-dominated reefs by controlling algae and provisioning space for the recruitment of corals. We observed large functional differences among two genera of parrotfishes that were driven by differences in diet. Fishes in the genus Scarus targeted filamentous algal turf assemblages, crustose coralline algae, and endolithic algae and avoided macroalgae, while fishes in the genus Sparisoma preferentially targeted macroalgae. However, species with similar diets were dissimilar in other attributes, including the habitats they frequented, the types of substrate they fed from, and the spatial scale at which they foraged. These differences indicate that species that appear to be functionally redundant when looking at diet alone exhibit high levels of complementarity when we consider multiple functional traits. By identifying key functional differences among parrotfishes, we provide critical information needed to manage parrotfishes to enhance the resilience of coral-dominated reefs and reverse phase shifts on algal-dominated reefs throughout the wider Caribbean. Further, our study provides a framework for predicting the impacts of consumer losses in other species rich ecosystems.

  14. Resource partitioning along multiple niche axes drives functional diversity in parrotfishes on Caribbean coral reefs.

    Science.gov (United States)

    Adam, Thomas C; Kelley, Megan; Ruttenberg, Benjamin I; Burkepile, Deron E

    2015-12-01

    The recent loss of key consumers to exploitation and habitat degradation has significantly altered community dynamics and ecosystem function across many ecosystems worldwide. Predicting the impacts of consumer losses requires knowing the level of functional diversity that exists within a consumer assemblage. In this study, we document functional diversity among nine species of parrotfishes on Caribbean coral reefs. Parrotfishes are key herbivores that facilitate the maintenance and recovery of coral-dominated reefs by controlling algae and provisioning space for the recruitment of corals. We observed large functional differences among two genera of parrotfishes that were driven by differences in diet. Fishes in the genus Scarus targeted filamentous algal turf assemblages, crustose coralline algae, and endolithic algae and avoided macroalgae, while fishes in the genus Sparisoma preferentially targeted macroalgae. However, species with similar diets were dissimilar in other attributes, including the habitats they frequented, the types of substrate they fed from, and the spatial scale at which they foraged. These differences indicate that species that appear to be functionally redundant when looking at diet alone exhibit high levels of complementarity when we consider multiple functional traits. By identifying key functional differences among parrotfishes, we provide critical information needed to manage parrotfishes to enhance the resilience of coral-dominated reefs and reverse phase shifts on algal-dominated reefs throughout the wider Caribbean. Further, our study provides a framework for predicting the impacts of consumer losses in other species rich ecosystems. PMID:26245147

  15. Global canonical symmetry in a quantum system

    Institute of Scientific and Technical Information of China (English)

    李子平

    1996-01-01

    Based on the phase-space path integral for a system with a regular or singular Lagrangian the generalized canonical Ward identities under the global symmetry transformation in extended phase space are deduced respectively, thus the relations among Green functions can be found. The connection between canonical symmetries and conservation laws at the quantum level is established. It is pointed out that this connection in classical theories, in general, is no longer always preserved in quantum theories. The advantage of our formulation is that we do not need to carry out the integration over the canonical momenta in phase-space generating functional as usually performed. A precise discussion of quantization for a nonlinear sigma model with Hopf and Chern-Simons terms is reexamined. The property of fractional spin at quantum level has been clarified.

  16. Thermodynamic extension of density-functional theory. I. Canonical Massieu-Planck function, its Legendre and Massieu-Planck transforms for equilibrium state in terms of density matrix

    CERN Document Server

    Balawender, Robert

    2009-01-01

    A unified formulation of the equilibrium state of a many-electron system in terms of an ensemble (mixed-state) density matrix, which applies the maximum entropy principle combined with the use of Massieu-Planck function, is presented. The properties of the characteristic functionals for macrocanonical ensemble are established. Their extension to other ensembles is accomplished via a Legendre transform. The relations between equilibrium states defined by a formal mathematical procedure and by criteria adopted for traditional (Gibbs, Helmholtz) potentials are investigated using Massieu-Planck transform. The preeminence of the Massieu-Planck function over the traditional thermodynamic potentials is discussed in detail on an example of their second derivatives. Introduced functions are suitable for application to the extensions of the density functional theory, both at finite and zero temperatures.

  17. 2D Quantum Gravity on Compact Riemann Surfaces and Two-Loop Partition Function: Circumventing the c=1 Barrier?

    CERN Document Server

    Bilal, Adel

    2014-01-01

    We study two-dimensional quantum gravity on arbitrary genus Riemann surfaces in the Kaehler formalism where the basic quantum field is the (Laplacian of the) Kaehler potential. We do a careful first-principles computation of the fixed-area partition function $Z[A]$ up to and including all two-loop contributions. This includes genuine two-loop diagrams as determined by the Liouville action, one-loop diagrams resulting from the non-trivial measure on the space of metrics, as well as one-loop diagrams involving various counterterm vertices. Contrary to what is often believed, several such counterterms, in addition to the usual cosmological constant, do and must occur. We consistently determine the relevant counterterms from a one-loop computation of the full two-point Green's function of the Kaehler field. Throughout this paper we use the general spectral cutoff regularization developed recently and which is well-suited for multi-loop computations on curved manifolds. At two loops, while all "unwanted" contribut...

  18. Canonical Ensemble Model for Black Hole Radiation

    Indian Academy of Sciences (India)

    Jingyi Zhang

    2014-09-01

    In this paper, a canonical ensemble model for the black hole quantum tunnelling radiation is introduced. In this model the probability distribution function corresponding to the emission shell is calculated to second order. The formula of pressure and internal energy of the thermal system is modified, and the fundamental equation of thermodynamics is also discussed.

  19. Canonical Quantization of Higher-Order Lagrangians

    Directory of Open Access Journals (Sweden)

    Khaled I. Nawafleh

    2011-01-01

    Full Text Available After reducing a system of higher-order regular Lagrangian into first-order singular Lagrangian using constrained auxiliary description, the Hamilton-Jacobi function is constructed. Besides, the quantization of the system is investigated using the canonical path integral approximation.

  20. Temporal energy partitions of Florida extreme sea level events as a function of Atlantic multidecadal oscillation

    Directory of Open Access Journals (Sweden)

    J. Park

    2010-06-01

    Full Text Available An energy-conservative metric based on the discrete wavelet transform is applied to assess the relative energy distribution of extreme sea level events across different temporal scales. The metric is applied to coastal events at Key West and Pensacola Florida as a function of two Atlantic Multidecadal Oscillation (AMO regimes. Under AMO warm conditions there is a small but significant redistribution of event energy from nearly static into more dynamic (shorter duration timescales at Key West, while at Pensacola the AMO-dependent changes in temporal event behaviour are less pronounced. Extreme events with increased temporal dynamics might be consistent with an increase in total energy of event forcings which may be a reflection of more energetic storm events during AMO warm phases. As dynamical models mature to the point of providing regional climate index predictability, coastal planners may be able to consider such temporal change metrics in planning scenarios.

  1. Temporal energy partitions of Florida extreme sea level events as a function of Atlantic multidecadal oscillation

    Directory of Open Access Journals (Sweden)

    J. Park

    2010-03-01

    Full Text Available An energy-conservative metric based on the discrete wavelet transform is applied to assess the relative energy distribution of non-stationary extreme sea level events across different temporal scales. The metric is applied to coastal events at Key West and Pensacola Florida as a function of two Atlantic Multidecadal Oscillation (AMO regimes. Under AMO warm conditions there is a small but significant redistribution of event energy from nearly static into more dynamic timescales at Key West, while at Pensacola the AMO-dependent changes in temporal event behaviour are less pronounced. Extreme events with increased temporal dynamics are consistent with an increase in total energy of event forcings which may be a reflection of more energetic storm events during AMO warm phases. As dynamical models mature to the point of providing regional climate index predictability, coastal planners may be able to consider such temporal change metrics in planning scenarios.

  2. Genome reconstructions indicate the partitioning of ecological functions inside a phytoplankton bloom in the Amundsen Sea, Antarctica

    Directory of Open Access Journals (Sweden)

    Tom O Delmont

    2015-10-01

    Full Text Available Antarctica polynyas support intense phytoplankton blooms, impacting their environment by a substantial depletion of inorganic carbon and nutrients. These blooms are dominated by the colony-forming haptophyte Phaeocystis antarctica and they are accompanied by a distinct bacterial population. Yet, the ecological role these bacteria may play in P. antarctica blooms awaits elucidation of their functional gene pool and of the geochemical activities they support. Here, we report on a metagenome (῀160 million reads analysis of the microbial community associated with a P. antarctica bloom event in the Amundsen Sea polynya (West Antarctica. Genomes of the most abundant Bacteroidetes and Proteobacteria populations have been reconstructed and a network analysis indicates a strong functional partitioning of these bacterial taxa. Three of them (SAR92, and members of the Oceanospirillaceae and Cryomorphaceae are found in close association with P. antarctica colonies. Distinct features of their carbohydrate, nitrogen, sulfur and iron metabolisms may serve to support mutualistic relationships with P. antarctica. The SAR92 genome indicates a specialization in the degradation of fatty acids and dimethylsulfoniopropionate (compounds released by P. antarctica into dimethyl sulfide, an aerosol precursor. The Oceanospirillaceae genome carries genes that may enhance algal physiology (cobalamin synthesis. Finally, the Cryomorphaceae genome is enriched in genes that function in cell or colony invasion. A novel pico-eukaryote, Micromonas related genome (19.6 Mb, ~94% completion was also recovered. It contains the gene for an anti-freeze protein, which is lacking in Micromonas at lower latitudes. These draft genomes are representative for abundant microbial taxa across the Southern Ocean surface.

  3. Moduli spaces of framed symplectic and orthogonal bundles on P2 and the K-theoretic Nekrasov partition functions

    Science.gov (United States)

    Choy, Jaeyoo

    2016-08-01

    Let K be the compact Lie group USp(N / 2) or SO(N , R) . Let MnK be the moduli space of framed K-instantons over S4 with the instanton number n. By Donaldson (1984), MnK is endowed with a natural scheme structure. It is a Zariski open subset of a GIT quotient of μ-1(0) , where μ is a holomorphic moment map such that μ-1(0) consists of the ADHM data. The purpose of the paper is to study the geometric properties of μ-1(0) and its GIT quotient, such as complete intersection, irreducibility, reducedness and normality. If K = USp(N / 2) then μ is flat and μ-1(0) is an irreducible normal variety for any n and even N. If K = SO(N , R) the similar results are proven for low n and N. As an application one can obtain a mathematical interpretation of the K-theoretic Nekrasov partition function of Nekrasov and Shadchin (2004).

  4. Partition coefficients for iron between plagioclase and basalt as a function of oxygen fugacity - Implications for Archean and lunar anorthosites

    Science.gov (United States)

    Phinney, W. C.

    1992-01-01

    As a prelude to determinations of the content of total iron as FeO(T) in melts in equilibrium with calcic anorthosites, the partition coefficients (Ds) for FeO(T) between calcic plagioclase and basaltic melt were determined, as a function of oxygen fugacity (f(O2)), for a basaltic composition that occurs as matrices for plagioclase megacrysts. Results showed that, at the liquidus conditions, the value of D for FeO(T) between calcic plagioclase and tholeiitic basalt changed little (from 0.030 to 0.044) between the very low f(O2) of the iron-wustite buffer and that of the quartz-fayalite-magnetite (QFM) buffer. At fugacities above QFM, the value for D increased rapidly to 0.14 at the magnetite-hematite buffer and to 0.33 in air. The increase in D results from the fact that, at f(O2) below QFM, nearly all of the Fe is in the Fe(2+) state; above QFM, the Fe(3+)/Fe(2+) ratio in the melt increases rapidly, causing more Fe to enter the plagioclase which accepts Fe(3+) more readily than Fe(2+).

  5. Vortex partition functions, wall crossing and equivariant Gromov-Witten invariants

    CERN Document Server

    Bonelli, Giulio; Tanzini, Alessandro; Vasko, Petr

    2013-01-01

    In this paper we identify the problem of equivariant vortex counting in a (2,2) supersymmetric two dimensional quiver gauged linear sigma model with that of computing the equivariant Gromov-Witten invariants of the GIT quotient target space determined by the quiver. We provide new contour integral formulae for the I and J-functions encoding the equivariant quantum cohomology of the target space. Its chamber structure is shown to be encoded in the analytical properties of the integrand. This is explained both via general arguments and by checking several key cases. We show how several results in equivariant Gromov-Witten theory follow just by deforming the integration contour. In particular we apply our formalism to compute Gromov-Witten invariants of the C^3/Z_n orbifold and of the Uhlembeck (partial) compactification of the moduli space of instantons on C^2. Moreover, we analyse dualities of quantum cohomology rings of holomorphic vector bundles over Grassmannians, which are relevant to BPS Wilson loop algeb...

  6. 2D quantum gravity on compact Riemann surfaces and two-loop partition function: A first principles approach

    Directory of Open Access Journals (Sweden)

    Adel Bilal

    2015-07-01

    Full Text Available We study two-dimensional quantum gravity on arbitrary genus Riemann surfaces in the Kähler formalism where the basic quantum field is the (Laplacian of the Kähler potential. We do a careful first-principles computation of the fixed-area partition function Z[A] up to and including all two-loop contributions. This includes genuine two-loop diagrams as determined by the Liouville action, one-loop diagrams resulting from the non-trivial measure on the space of metrics, as well as one-loop diagrams involving various counterterm vertices. Contrary to what is often believed, several such counterterms, in addition to the usual cosmological constant, do and must occur. We consistently determine the relevant counterterms from a one-loop computation of the full two-point Green's function of the Kähler field. Throughout this paper we use the general spectral cutoff regularization developed recently and which is well-suited for multi-loop computations on curved manifolds. At two loops, while all “unwanted” contributions to ln⁡(Z[A]/Z[A0] correctly cancel, it appears that the finite coefficient of ln⁡(A/A0 does depend on the finite part of a certain counterterm coefficient, i.e. on the finite renormalization conditions one has to impose. There exists a choice that reproduces the famous KPZ-scaling, but it seems to be only one consistent choice among others. Maybe, this hints at the possibility that other renormalization conditions could eventually provide a way to circumvent the famous c=1 barrier.

  7. 2D quantum gravity on compact Riemann surfaces and two-loop partition function: A first principles approach

    Science.gov (United States)

    Bilal, Adel; Leduc, Laetitia

    2015-07-01

    We study two-dimensional quantum gravity on arbitrary genus Riemann surfaces in the Kähler formalism where the basic quantum field is the (Laplacian of the) Kähler potential. We do a careful first-principles computation of the fixed-area partition function Z [ A ] up to and including all two-loop contributions. This includes genuine two-loop diagrams as determined by the Liouville action, one-loop diagrams resulting from the non-trivial measure on the space of metrics, as well as one-loop diagrams involving various counterterm vertices. Contrary to what is often believed, several such counterterms, in addition to the usual cosmological constant, do and must occur. We consistently determine the relevant counterterms from a one-loop computation of the full two-point Green's function of the Kähler field. Throughout this paper we use the general spectral cutoff regularization developed recently and which is well-suited for multi-loop computations on curved manifolds. At two loops, while all "unwanted" contributions to ln ⁡ (Z [ A ] / Z [A0 ]) correctly cancel, it appears that the finite coefficient of ln ⁡ (A /A0) does depend on the finite part of a certain counterterm coefficient, i.e. on the finite renormalization conditions one has to impose. There exists a choice that reproduces the famous KPZ-scaling, but it seems to be only one consistent choice among others. Maybe, this hints at the possibility that other renormalization conditions could eventually provide a way to circumvent the famous c = 1 barrier.

  8. Improved methods for Feynman path integral calculations and their application to calculate converged vibrational-rotational partition functions, free energies, enthalpies, entropies, and heat capacities for methane.

    Science.gov (United States)

    Mielke, Steven L; Truhlar, Donald G

    2015-01-28

    We present an improved version of our "path-by-path" enhanced same path extrapolation scheme for Feynman path integral (FPI) calculations that permits rapid convergence with discretization errors ranging from O(P(-6)) to O(P(-12)), where P is the number of path discretization points. We also present two extensions of our importance sampling and stratified sampling schemes for calculating vibrational-rotational partition functions by the FPI method. The first is the use of importance functions for dihedral angles between sets of generalized Jacobi coordinate vectors. The second is an extension of our stratification scheme to allow some strata to be defined based only on coordinate information while other strata are defined based on both the geometry and the energy of the centroid of the Feynman path. These enhanced methods are applied to calculate converged partition functions by FPI methods, and these results are compared to ones obtained earlier by vibrational configuration interaction (VCI) calculations, both calculations being for the Jordan-Gilbert potential energy surface. The earlier VCI calculations are found to agree well (within ∼1.5%) with the new benchmarks. The FPI partition functions presented here are estimated to be converged to within a 2σ statistical uncertainty of between 0.04% and 0.07% for the given potential energy surface for temperatures in the range 300-3000 K and are the most accurately converged partition functions for a given potential energy surface for any molecule with five or more atoms. We also tabulate free energies, enthalpies, entropies, and heat capacities.

  9. The dimer partition function

    OpenAIRE

    Pesando, I.

    1993-01-01

    We apply the Ginzburg criterion to the dimer problem and we solve the apparent contradiction of a system with mean field $\\alpha={1\\over2}$, the typical value of tricritical systems, and upper critical dimension $D_{cr}=6$. We find that the system has upper critical dimension $D_{cr}=6$ , while for $D\\le4$ it should undergo a first order phase transition. We comment on the latter wrong result examining the approximation we used.

  10. Physical states in the canonical tensor model from the perspective of random tensor networks

    CERN Document Server

    Narain, Gaurav; Sato, Yuki

    2014-01-01

    Tensor models, generalization of matrix models, are studied aiming for quantum gravity in dimensions larger than two. Among them, the canonical tensor model is formulated as a totally constrained system with first-class constraints, the algebra of which resembles the Dirac algebra of general relativity. When quantized, the physical states are defined to be vanished by the quantized constraints. In explicit representations, the constraint equations are a set of partial differential equations for physical wave-functions, which do not seem straightforward to solve due to their non-linear character. In this paper, after providing some explicit solutions for N = 2,3, we show that certain scale-free integration of partition functions of statistical systems on random networks, or random tensor networks more generally, provides a series of solutions for general N. Then, by generalizing this form, we also obtain various solutions for general N. Moreover, we show that the solutions for the cases with a cosmological con...

  11. Partitions with Initial Repetitions

    Institute of Scientific and Technical Information of China (English)

    George E. ANDREWS

    2009-01-01

    A variety of interesting connections with modular forms, mock theta functions and Rogers-Ramanujan type identities arise in consideration of partitions in which the smaller integers are repeated as summands more often than the larger summands. In particular, this concept leads to new interpre-tations of the Rogers-Selberg identities and Bailey's modulus 9 identities.

  12. The Partition Function of the Dirichlet Operator D2s=∑i=1d‍(-∂i2s on a d-Dimensional Rectangle Cavity

    Directory of Open Access Journals (Sweden)

    Agapitos N. Hatzinikitas

    2015-01-01

    Full Text Available We study the asymptotic behavior of the free partition function in the t→0+ limit for a diffusion process which consists of d-independent, one-dimensional, symmetric, 2s-stable processes in a hyperrectangular cavity K⊂Rd with an absorbing boundary. Each term of the partition function for this polyhedron in d-dimensions can be represented by a quermassintegral and the geometrical information conveyed by the eigenvalues of the fractional Dirichlet Laplacian for this solvable model is now transparent. We also utilize the intriguing method of images to solve the same problem, in one and two dimensions, and recover identical results to those derived in the previous analysis.

  13. The AdS/CFT partition function, AdS as a lift of a CFT, and holographic RG flow from conformal deformations

    CERN Document Server

    Cantrell, Sean

    2015-01-01

    Conformal deformations manifest in the AdS/CFT correspondence as boundary conditions on the AdS field. Heretofore, double-trace deformations have been the primary focus in this context. To better understand multitrace deformations, we revisit the relationship between the generating AdS partition function for a free bulk theory and the boundary CFT partition function subject to arbitrary conformal deformations. The procedure leads us to a formalism that constructs bulk fields from boundary operators. Using this formalism, we independently replicate the holographic RG flow narrative to go on to interpret the brane used to regulate the AdS theory as a renormalization scale. The scale-dependence of the dilatation spectrum of a boundary theory in the presence of general deformations can be thus understood on the AdS side using this formalism.

  14. Cavity partition and functionalization of a [2+3] organic molecular cage by inserting polar P[double bond, length as m-dash]O bonds.

    Science.gov (United States)

    Feng, Genfeng; Liu, Wei; Peng, Yuxin; Zhao, Bo; Huang, Wei; Dai, Yafei

    2016-07-28

    The cavity of a [2+3] organic molecular cage was partitioned and functionalized by inserting inner-directed P[double bond, length as m-dash]O bonds, which shows CO2 capture and CH4 exclusion due to the size-matching and polarity effects. Computational results demonstrate that the successful segmentation via polar P[double bond, length as m-dash]O bonds facilitates the CO2 molecules to reside selectively inside the cavity. PMID:27356151

  15. Symmetric Quartic Map in natural canonical coordinates

    Science.gov (United States)

    Baldwin, Danielle; Jones, Bilal; Settle, Talise; Ali, Halima; Punjabi, Alkesh

    2015-11-01

    The generating function for the simple map is modified by replacing the cubic term in canonical momentum by a quartic term. New parameters are introduced in the modified generating function to control the height and the width of ideal separatrix surface and the poloidal magnetic flux inside ideal separatrix. The new generating function is the generating function for the Symmetric Quartic Map (SQM). The new parameters in the generating function are chosen such that the height, width, elongation, and the poloidal flux inside the separatrix for the SQM are same as the simple map. The resulting generating function for the SQM is then transformed from the physical coordinates to the natural canonical coordinates. The equilibrium separatrix of the SQM is calculated in the natural canonical coordinates. The purpose of this research is to calculate the homoclinic tangle of the SQM and compare with the simple map. The separatrix of the simple map is open and unbounded; while the separatrix of the SQM is closed and compact. Motivation is to see what role the topology of the separatrix plays in its homoclinic tangle in single-null divertor tokamaks. This work is supported by grants DE-FG02-01ER54624, DE-FG02-04ER54793, and DE-FG02-07ER54937.

  16. Physical states in the canonical tensor model from the perspective of random tensor networks

    Science.gov (United States)

    Narain, Gaurav; Sasakura, Naoki; Sato, Yuki

    2015-01-01

    Tensor models, generalization of matrix models, are studied aiming for quantum gravity in dimensions larger than two. Among them, the canonical tensor model is formulated as a totally constrained system with first-class constraints, the algebra of which resembles the Dirac algebra of general relativity. When quantized, the physical states are defined to be vanished by the quantized constraints. In explicit representations, the constraint equations are a set of partial differential equations for the physical wave-functions, which do not seem straightforward to be solved due to their non-linear character. In this paper, after providing some explicit solutions for N = 2 , 3, we show that certain scale-free integration of partition functions of statistical systems on random networks (or random tensor networks more generally) provides a series of solutions for general N. Then, by generalizing this form, we also obtain various solutions for general N. Moreover, we show that the solutions for the cases with a cosmological constant can be obtained from those with no cosmological constant for increased N. This would imply the interesting possibility that a cosmological constant can always be absorbed into the dynamics and is not an input parameter in the canonical tensor model. We also observe the possibility of symmetry enhancement in N = 3, and comment on an extension of Airy function related to the solutions.

  17. Canonical correlations between chemical and energetic characteristics of lignocellulosic wastes

    Directory of Open Access Journals (Sweden)

    Thiago de Paula Protásio

    2012-09-01

    Full Text Available Canonical correlation analysis is a statistical multivariate procedure that allows analyzing linear correlation that may exist between two groups or sets of variables (X and Y. This paper aimed to provide canonical correlation analysis between a group comprised of lignin and total extractives contents and higher heating value (HHV with a group of elemental components (carbon, hydrogen, nitrogen and sulfur for lignocellulosic wastes. The following wastes were used: eucalyptus shavings; pine shavings; red cedar shavings; sugar cane bagasse; residual bamboo cellulose pulp; coffee husk and parchment; maize harvesting wastes; and rice husk. Only the first canonical function was significant, but it presented a low canonical R². High carbon, hydrogen and sulfur contents and low nitrogen contents seem to be related to high total extractives contents of the lignocellulosic wastes. The preliminary results found in this paper indicate that the canonical correlations were not efficient to explain the correlations between the chemical elemental components and lignin contents and higher heating values.

  18. Canonical cortical circuits: current evidence and theoretical implications

    Directory of Open Access Journals (Sweden)

    Capone F

    2016-04-01

    Full Text Available Fioravante Capone,1,2 Matteo Paolucci,1,2 Federica Assenza,1,2 Nicoletta Brunelli,1,2 Lorenzo Ricci,1,2 Lucia Florio,1,2 Vincenzo Di Lazzaro1,2 1Unit of Neurology, Neurophysiology, Neurobiology, Department of Medicine, Università Campus Bio-Medico di Roma, Rome, Italy; 2Fondazione Alberto Sordi – Research Institute for Aging, Rome, ItalyAbstract: Neurophysiological and neuroanatomical studies have found that the same basic structural and functional organization of neuronal circuits exists throughout the cortex. This kind of cortical organization, termed canonical circuit, has been functionally demonstrated primarily by studies involving visual striate cortex, and then, the concept has been extended to different cortical areas. In brief, the canonical circuit is composed of superficial pyramidal neurons of layers II/III receiving different inputs and deep pyramidal neurons of layer V that are responsible for cortex output. Superficial and deep pyramidal neurons are reciprocally connected, and inhibitory interneurons participate in modulating the activity of the circuit. The main intuition of this model is that the entire cortical network could be modeled as the repetition of relatively simple modules composed of relatively few types of excitatory and inhibitory, highly interconnected neurons. We will review the origin and the application of the canonical cortical circuit model in the six sections of this paper. The first section (The origins of the concept of canonical circuit: the cat visual cortex reviews the experiments performed in the cat visual cortex, from the origin of the concept of canonical circuit to the most recent developments in the modelization of cortex. The second (The canonical circuit in neocortex and third (Toward a canonical circuit in agranular cortex sections try to extend the concept of canonical circuit to other cortical areas, providing some significant examples of circuit functioning in different cytoarchitectonic

  19. Canonical quantization of constrained systems

    Energy Technology Data Exchange (ETDEWEB)

    Bouzas, A.; Epele, L.N.; Fanchiotti, H.; Canal, C.A.G. (Laboratorio de Fisica Teorica, Departamento de Fisica, Universidad Nacional de La Plata, Casilla de Correo No. 67, 1900 La Plata, Argentina (AR))

    1990-07-01

    The consideration of first-class constraints together with gauge conditions as a set of second-class constraints in a given system is shown to be incorrect when carrying out its canonical quantization.

  20. The canon as text for a biblical theology

    Directory of Open Access Journals (Sweden)

    James A. Loader

    2005-10-01

    Full Text Available The novelty of the canonical approach is questioned and its fascination at least partly traced to the Reformation, as well as to the post-Reformation’s need for a clear and authoritative canon to perform the function previously performed by the church. This does not minimise the elusiveness and deeply contradictory positions both within the canon and triggered by it. On the one hand, the canon itself is a centripetal phenomenon and does play an important role in exegesis and theology. Even so, on the other hand, it not only contains many difficulties, but also causes various additional problems of a formal as well as a theological nature. The question is mooted whether the canonical approach alleviates or aggravates the dilemma. Since this approach has become a major factor in Christian theology, aspects of the Christian canon are used to gauge whether “canon” is an appropriate category for eliminating difficulties that arise by virtue of its own existence. Problematic uses and appropriations of several Old Testament canons are advanced, as well as evidence in the New Testament of a consciousness that the “old” has been surpassed(“Überbietungsbewußtsein”. It is maintained that at least the Childs version of the canonical approach fails to smooth out these and similar difficulties. As a method it can cater for the New Testament’s (superior role as the hermeneutical standard for evaluating the Old, but flounders on its inability to create the theological unity it claims can solve religious problems exposed by Old Testament historical criticism. It is concluded that canon as a category cannot be dispensed with, but is useful for the opposite of the purpose to which it is conventionally put: far from bringing about theological “unity” or producing a standard for “correct” exegesis, it requires different readings of different canons.

  1. Critical adsorption and critical Casimir forces in the canonical ensemble.

    Science.gov (United States)

    Gross, Markus; Vasilyev, Oleg; Gambassi, Andrea; Dietrich, S

    2016-08-01

    Critical properties of a liquid film between two planar walls are investigated in the canonical ensemble, within which the total number of fluid particles, rather than their chemical potential, is kept constant. The effect of this constraint is analyzed within mean-field theory (MFT) based on a Ginzburg-Landau free-energy functional as well as via Monte Carlo simulations of the three-dimensional Ising model with fixed total magnetization. Within MFT and for finite adsorption strengths at the walls, the thermodynamic properties of the film in the canonical ensemble can be mapped exactly onto a grand canonical ensemble in which the corresponding chemical potential plays the role of the Lagrange multiplier associated with the constraint. However, due to a nonintegrable divergence of the mean-field order parameter profile near a wall, the limit of infinitely strong adsorption turns out to be not well-defined within MFT, because it would necessarily violate the constraint. The critical Casimir force (CCF) acting on the two planar walls of the film is generally found to behave differently in the canonical and grand canonical ensembles. For instance, the canonical CCF in the presence of equal preferential adsorption at the two walls is found to have the opposite sign and a slower decay behavior as a function of the film thickness compared to its grand canonical counterpart. We derive the stress tensor in the canonical ensemble and find that it has the same expression as in the grand canonical case, but with the chemical potential playing the role of the Lagrange multiplier associated with the constraint. The different behavior of the CCF in the two ensembles is rationalized within MFT by showing that, for a prescribed value of the thermodynamic control parameter of the film, i.e., density or chemical potential, the film pressures are identical in the two ensembles, while the corresponding bulk pressures are not. PMID:27627242

  2. Critical adsorption and critical Casimir forces in the canonical ensemble

    Science.gov (United States)

    Gross, Markus; Vasilyev, Oleg; Gambassi, Andrea; Dietrich, S.

    2016-08-01

    Critical properties of a liquid film between two planar walls are investigated in the canonical ensemble, within which the total number of fluid particles, rather than their chemical potential, is kept constant. The effect of this constraint is analyzed within mean-field theory (MFT) based on a Ginzburg-Landau free-energy functional as well as via Monte Carlo simulations of the three-dimensional Ising model with fixed total magnetization. Within MFT and for finite adsorption strengths at the walls, the thermodynamic properties of the film in the canonical ensemble can be mapped exactly onto a grand canonical ensemble in which the corresponding chemical potential plays the role of the Lagrange multiplier associated with the constraint. However, due to a nonintegrable divergence of the mean-field order parameter profile near a wall, the limit of infinitely strong adsorption turns out to be not well-defined within MFT, because it would necessarily violate the constraint. The critical Casimir force (CCF) acting on the two planar walls of the film is generally found to behave differently in the canonical and grand canonical ensembles. For instance, the canonical CCF in the presence of equal preferential adsorption at the two walls is found to have the opposite sign and a slower decay behavior as a function of the film thickness compared to its grand canonical counterpart. We derive the stress tensor in the canonical ensemble and find that it has the same expression as in the grand canonical case, but with the chemical potential playing the role of the Lagrange multiplier associated with the constraint. The different behavior of the CCF in the two ensembles is rationalized within MFT by showing that, for a prescribed value of the thermodynamic control parameter of the film, i.e., density or chemical potential, the film pressures are identical in the two ensembles, while the corresponding bulk pressures are not.

  3. BKP plane partitions

    Energy Technology Data Exchange (ETDEWEB)

    Foda, Omar; Wheeler, Michael [Department of Mathematics and Statistics, University of Melbourne, Parkville, Victoria 3010 (Australia)

    2007-01-15

    Using BKP neutral fermions, we derive a product expression for the generating function of volume-weighted plane partitions that satisfy two conditions. If we call a set of adjacent equal height-h columns, h > 0, an h-path, then 1. Every h-path can assume one of two possible colours. 2. There is a unique way to move along an h-path from any column to another.

  4. BKP plane partitions

    OpenAIRE

    Foda, O.; Wheeler, M.

    2006-01-01

    Using BKP neutral fermions, we derive a product expression for the generating function of volume-weighted plane partitions that satisfy two conditions. If we call a set of adjacent equal height-h columns, h > 0, an h-path, then 1. Every h-path can assume one of two possible colours. 2. There is a unique way to move along an h-path from any column to another.

  5. BKP plane partitions

    International Nuclear Information System (INIS)

    Using BKP neutral fermions, we derive a product expression for the generating function of volume-weighted plane partitions that satisfy two conditions. If we call a set of adjacent equal height-h columns, h > 0, an h-path, then 1. Every h-path can assume one of two possible colours. 2. There is a unique way to move along an h-path from any column to another

  6. Canonical Approaches to Applications of the Virial Theorem.

    Science.gov (United States)

    Walton, Jay R; Rivera-Rivera, Luis A; Lucchese, Robert R; Bevan, John W

    2016-02-11

    Canonical approaches are applied for investigation of the extraordinarily accurate electronic ground state potentials of H2(+), H2, HeH(+), and LiH using the virial theorem. These approaches will be dependent on previous investigations involving the canonical nature of E(R), the Born-Oppenheimer potential, and F(R), the associated force of E(R), that have been demonstrated to be individually canonical to high accuracy in the case of the systems investigated. Now, the canonical nature of the remaining functions in the virial theorem [the electronic kinetic energy T(R), the electrostatic potential energy V(R), and the function W(R) = RF(R)] are investigated and applied to H2, HeH(+), and LiH with H2(+) chosen as reference. The results will be discussed in the context of a different perspective of molecular bonding that goes beyond previous direct applications of the virial theorem. PMID:26788937

  7. Canonical Approaches to Applications of the Virial Theorem.

    Science.gov (United States)

    Walton, Jay R; Rivera-Rivera, Luis A; Lucchese, Robert R; Bevan, John W

    2016-02-11

    Canonical approaches are applied for investigation of the extraordinarily accurate electronic ground state potentials of H2(+), H2, HeH(+), and LiH using the virial theorem. These approaches will be dependent on previous investigations involving the canonical nature of E(R), the Born-Oppenheimer potential, and F(R), the associated force of E(R), that have been demonstrated to be individually canonical to high accuracy in the case of the systems investigated. Now, the canonical nature of the remaining functions in the virial theorem [the electronic kinetic energy T(R), the electrostatic potential energy V(R), and the function W(R) = RF(R)] are investigated and applied to H2, HeH(+), and LiH with H2(+) chosen as reference. The results will be discussed in the context of a different perspective of molecular bonding that goes beyond previous direct applications of the virial theorem.

  8. Solve the partitioning problem by sticker model in DNA computing

    Institute of Scientific and Technical Information of China (English)

    QU Huiqin; LU Mingming; ZHU Hong

    2004-01-01

    The aim of this work is to solve the partitioning problem, the most canonical NP-complete problem containing numerical parameters, within the sticker model of DNA computing. We firstly design a parallel program for addition, and then give a program to calculate the subset sums of a set. At last, a program for partitioning is given, which contains the former programs. Furthermore, the correctness of each program is proved in this paper.

  9. Determinant representation of the domain-wall boundary condition partition function of a Richardson-Gaudin model containing one arbitrary spin

    Science.gov (United States)

    Faribault, Alexandre; Tschirhart, Hugo; Muller, Nicolas

    2016-05-01

    In this work we present a determinant expression for the domain-wall boundary condition partition function of rational (XXX) Richardson-Gaudin models which, in addition to N-1 spins \\frac{1}{2}, contains one arbitrarily large spin S. The proposed determinant representation is written in terms of a set of variables which, from previous work, are known to define eigenstates of the quantum integrable models belonging to this class as solutions to quadratic Bethe equations. Such a determinant can be useful numerically since systems of quadratic equations are much simpler to solve than the usual highly nonlinear Bethe equations. It can therefore offer significant gains in stability and computation speed.

  10. Canonical formalism for coupled beam optics

    Energy Technology Data Exchange (ETDEWEB)

    Kheifets, S.A.

    1989-09-01

    Beam optics of a lattice with an inter-plane coupling is treated using canonical Hamiltonian formalism. The method developed is equally applicable both to a circular (periodic) machine and to an open transport line. A solution of the equation of a particle motion (and correspondingly transfer matrix between two arbitrary points of the lattice) are described in terms of two amplitude functions (and their derivatives and corresponding phases of oscillations) and four coupling functions, defined by a solution of the system of the first-order nonlinear differential equations derived in the paper. Thus total number of independent parameters is equal to ten. 8 refs.

  11. Periodicity, the Canon and Sport

    Directory of Open Access Journals (Sweden)

    Thomas F. Scanlon

    2015-10-01

    Full Text Available The topic according to this title is admittedly a broad one, embracing two very general concepts of time and of the cultural valuation of artistic products. Both phenomena are, in the present view, largely constructed by their contemporary cultures, and given authority to a great extent from the prestige of the past. The antiquity of tradition brings with it a certain cachet. Even though there may be peripheral debates in any given society which question the specifics of periodization or canonicity, individuals generally accept the consensus designation of a sequence of historical periods and they accept a list of highly valued artistic works as canonical or authoritative. We will first examine some of the processes of periodization and of canon-formation, after which we will discuss some specific examples of how these processes have worked in the sport of two ancient cultures, namely Greece and Mesoamerica.

  12. The Fibonacci partition triangles

    CERN Document Server

    Fahr, Philipp

    2011-01-01

    In two previous papers we have presented partition formulae for the Fibonacci numbers motivated by the appearance of the Fibonacci numbers in the representation theory of the 3-Kronecker quiver and its universal cover, the 3-regular tree. Here we show that the basic information can be rearranged in two triangles. They are quite similar to the Pascal triangle of the binomial coefficients, but in contrast to the additivity rule for the Pascal triangle, we now deal with additivity along hooks, or, equivalently, with additive functions for valued translation quivers. As for the Pascal triangle, we see that the numbers in these Fibonacci partition triangles are given by evaluating polynomials. We show that the two triangles can be obtained from each other by looking at differences of numbers, it is sufficient to take differences along arrows and knight's moves.

  13. Existence of log canonical closures

    CERN Document Server

    Hacon, Christopher D

    2011-01-01

    Let $f:X\\to U$ be a projective morphism of normal varieties and $(X,\\Delta)$ a dlt pair. We prove that if there is an open set $U^0\\subset U$, such that $(X,\\Delta)\\times_U U^0$ has a good minimal model over $U^0$ and the images of all the non-klt centers intersect $U^0$, then $(X,\\Delta)$ has a good minimal model over $U$. As consequences we show the existence of log canonical compactifications for open log canonical pairs, and the fact that the moduli functor of stable schemes satisfies the valuative criterion for properness.

  14. A New Spinel-Olivine Oxybarometer: Near-Liquidus Partitioning of V between Olivine-Melt, Spinel-Melt, and Spinel-Olivine in Martian Basalt Composition Y980459 as a Function of Oxygen Fugacity

    Science.gov (United States)

    Papike, J. J.; Le, L.; Burger, P. V.; Shearer, C. K.; Bell, A. S.; Jones, J.

    2013-01-01

    Our research on valence state partitioning began in 2005 with a review of Cr, Fe, Ti, and V partitioning among crystallographic sites in olivine, pyroxene, and spinel [1]. That paper was followed by several on QUE94201 melt composition and specifically on Cr, V, and Eu partitioning between pyroxene and melt [2-5]. This paper represents the continuation of our examination of the partitioning of multivalent V between olivine, spinel, and melt in martian olivine-phyric basalts of Y980459 composition [6, 7]. Here we introduce a new, potentially powerful oxybarometer, V partitioning between spinel and olivine, which can be used when no melt is preserved in the meteorite. The bulk composition of QUE94201 was ideal for our study of martian pyroxene-phyric basalts and specifically the partitioning between pyroxene-melt for Cr, V, and Eu. Likewise, bulk composition Y980459 is ideal for the study of martian olivine-phyric basalts and specifically for olivine-melt, spinel-melt, and spinel-olivine partitioning of V as a function of oxygen fugacity.

  15. Ionic partitioning and stomatal regulation: dissecting functional elements of the genotypic basis of salt stress adaptation in grafted melon.

    Science.gov (United States)

    Sanoubar, Rabab; Orsini, Francesco; Gianquinto, Giorgio

    2013-11-01

    Vegetable grafting is commonly claimed to improve crop's tolerance to biotic and abiotic stresses, including salinity. Although the use of inter-specific graftings is relatively common, whether the improved salt tolerance should be attributed to the genotypic background rather than the grafting per se is a matter of discussion among scientists. It is clear that most of published research has to date overlooked the issue, with the mutual presence of self-grafted and non-grafted controls resulting to be quite rare within experimental evidences. It was recently demonstrated that the genotype of the rootstock and grafting per se are responsible respectively for the differential ion accumulation and partitioning as well as to the stomatal adaptation to the stress. The present paper contributes to the ongoing discussion with further data on the differences associated to salinity response in a range of grafted melon combinations.

  16. A Comparative Study of Kernel and Robust Canonical Correlation Analysis

    Directory of Open Access Journals (Sweden)

    Ashad M. Alam

    2010-02-01

    Full Text Available A number of measures of canonical correlation coefficient are now used in multimedia related fields like object recognition, image segmentation facial expression recognition and pattern recognition in the different literature. Some robust forms of classical canonical correlation coefficient are introduced recently to address the robustness issue of the canonical coefficient in the presence of outliers and departure from normality. Also a few number of kernels are used in canonical analysis to capture nonlinear relationship in data space, which is linear in some higher dimensional feature space. But not much work has been done to investigate their relative performances through i simulation from the view point of sensitivity, breakdown analysis as well as ii using real data sets. In this paper an attempt has been made to compare performances of kernel canonical correlation coefficients (Gaussian function, Laplacian function and Polynomial function with that of robust and classical canonical correlation coefficient measures using simulation with five sample sizes (50, 500, 1000, 1500 and 2000, influence function, breakdown point along with several real data and a multi-modal data sets, focusing on the specific case of segmented images with associated text. We investigate the bias, mean square error(MISE, qualitative robustness index (RI, sensitivity curve of each estimator under a variety of situations and also employ box plots and scatter plots of canonical variates to judge their performances. We have observed that the class of kernel estimators perform better than the class of classical and robust estimators in general and the kernel estimator with Laplacian function has shown the best performance for large sample size and break down is high in case of nonlinear data.

  17. Romanticism, Sexuality, and the Canon.

    Science.gov (United States)

    Rowe, Kathleen K.

    1990-01-01

    Traces the Romanticism in the work and persona of film director Jean-Luc Godard. Examines the contradictions posed by Godard's politics and representations of sexuality. Asserts, that by bringing an ironic distance to the works of such canonized directors, viewers can take pleasure in those works despite their contradictions. (MM)

  18. Canonical Notch activation in osteocytes causes osteopetrosis.

    Science.gov (United States)

    Canalis, Ernesto; Bridgewater, David; Schilling, Lauren; Zanotti, Stefano

    2016-01-15

    Activation of Notch1 in cells of the osteoblastic lineage inhibits osteoblast differentiation/function and causes osteopenia, whereas its activation in osteocytes causes a distinct osteopetrotic phenotype. To explore mechanisms responsible, we established the contributions of canonical Notch signaling (Rbpjκ dependent) to osteocyte function. Transgenics expressing Cre recombinase under the control of the dentin matrix protein-1 (Dmp1) promoter were crossed with Rbpjκ conditional mice to generate Dmp1-Cre(+/-);Rbpjκ(Δ/Δ) mice. These mice did not have a skeletal phenotype, indicating that Rbpjκ is dispensable for osteocyte function. To study the Rbpjκ contribution to Notch activation, Rosa(Notch) mice, where a loxP-flanked STOP cassette is placed between the Rosa26 promoter and the NICD coding sequence, were crossed with Dmp1-Cre transgenic mice and studied in the context (Dmp1-Cre(+/-);Rosa(Notch);Rbpjκ(Δ/Δ)) or not (Dmp1-Cre(+/-);Rosa(Notch)) of Rbpjκ inactivation. Dmp1-Cre(+/-);Rosa(Notch) mice exhibited increased femoral trabecular bone volume and decreased osteoclasts and bone resorption. The phenotype was reversed in the context of the Rbpjκ inactivation, demonstrating that Notch canonical signaling was accountable for the phenotype. Notch activation downregulated Sost and Dkk1 and upregulated Axin2, Tnfrsf11b, and Tnfsf11 mRNA expression, and these effects were not observed in the context of the Rbpjκ inactivation. In conclusion, Notch activation in osteocytes suppresses bone resorption and increases bone volume by utilization of canonical signals that also result in the inhibition of Sost and Dkk1 and upregulation of Wnt signaling. PMID:26578715

  19. Life-cycle assessment of lightweight textile membrane partition walls

    OpenAIRE

    Neiva, Sara Daniela Oliveira; Mateus, Ricardo; Macieira, Mónica; Mendonça, Paulo, ed. lit.; Bragança, L.

    2012-01-01

    This paper analyze the environmental, functional and economical performances of some conceptual lightweights textiles membranes partitions walls and to compare one of them with two technologies present in Portuguese market: i) the heavyweight conventional hollow brick partition wall; and ii) the lightweight reference plasterboard partition wall. Advantages of use textile/ fibrous/ membrane based materials in partition walls are focused and they may contribute for the development of new partit...

  20. The partitioning of iodides into steam

    International Nuclear Information System (INIS)

    In order to estimate the likely releases of radioactive iodine during steam generator tube rupture (SGTR) faults, it is necessary to know the relevant partition coefficients as a function of temperature and solution composition. It has been suggested previously that, under SGTR fault conditions, partitioning of free or ion-paired I- into the steam may be more extensive than that for molecular HI. This report uses available information on the partitioning of iodides and other salts to provide a means of estimating the partition coefficient of the iodide ion as a function of boric acid concentration and temperature. (author)

  1. The role of the Wnt canonical signaling in neurodegenerative diseases.

    Science.gov (United States)

    Libro, Rosaliana; Bramanti, Placido; Mazzon, Emanuela

    2016-08-01

    The Wnt/β-catenin or Wnt canonical pathway controls multiple biological processes throughout development and adult life. Growing evidences have suggested that deregulation of the Wnt canonical pathway could be involved in the pathogenesis of neurodegenerative diseases. The Wnt canonical signaling is a pathway tightly regulated, which activation results in the inhibition of the Glycogen Synthase Kinase 3β (GSK-3β) function and in increased β-catenin activity, that migrates into the nucleus, activating the transcription of the Wnt target genes. Conversely, when the Wnt canonical pathway is turned off, increased levels of GSK-3β promote β-catenin degradation. Hence, GSK-3β could be considered as a key regulator of the Wnt canonical pathway. Of note, GSK-3β has also been involved in the modulation of inflammation and apoptosis, determining the delicate balance between immune tolerance/inflammation and neuronal survival/neurodegeneration. In this review, we have summarized the current acknowledgements about the role of the Wnt canonical pathway in the pathogenesis of some neurodegenerative diseases including Alzheimer's disease, cerebral ischemia, Parkinson's disease, Huntington's disease, multiple sclerosis and amyotrophic lateral sclerosis, with particular regard to the main in vitro and in vivo studies in this field, by reviewing 85 research articles about.

  2. Energy functionals and canonical metrics in Sasakian geometry%Sasaki几何中的能量泛函与典则度量

    Institute of Scientific and Technical Information of China (English)

    汪悦; 张希

    2011-01-01

    In this paper, we introduce Ek functional in Sasakian geometry, and deduce their Euler-Lagrange equations. Then, we prove the uniqueness results for critical metrics of these functionals. We also obtain some uniqueness results for Sasakian metrics with constantly transverse Ok curvature.%本文讨论了Sasaki几何中的能量泛函Ek,推导出其Euler-Lagrange方程,进而证明其临界度量的唯一性定理.另外,我们得到了具有常横截σk曲率的Sasaki度量的唯一性结论.

  3. Canonical and non-canonical pathways of osteoclast formation

    OpenAIRE

    Knowles, H.J.; Athanasou, N A

    2009-01-01

    Physiological and pathological bone resorption is mediated by osteoclasts, multinucleated cells which are formed by the fusion of monocyte / macrophage precursors. The canonical pathway of osteoclast formation requires the presence of the receptor activator for NFkB ligand (RANKL) and macrophage colony stimulating factor (M-CSF). Noncanonical pathways of osteoclast formation have been described in which cytokines / growth factors can substitute for RANKL or M-CSF to...

  4. Studies of n-Octanol/water Partition Coefficients (IgKow) for Organophosphate Compounds by Density Functional Theory

    Institute of Scientific and Technical Information of China (English)

    LIU Hong-Xia; WANG Zun-Yao; ZHAI Zhi-Cai; LIU Hong-Yan; WANG Lian-Sheng

    2007-01-01

    Optimized calculation of 35 dialkyl phenyl phosphate compounds (OPs) was carried out at the B3LYP/6-31G* level in Gaussian 98 program. Based on the theoretical linear solvation energy relationship (TLSER) model, the obtained parameters were taken as theoretical descriptors to establish the novel QSPR model for predicting n-octanol/water partition coefficients (IgKow) of OPs. The new model achieved in this work contains three variables, i.e., molecular volume (Vm),dipole moment of the molecules (μ) and enthalpy (H0). For this model, R2 = 0.9167 and SD = 0.31 at large t values. In addition, the variation inflation factors (VIF) of variables are all close to 1.0,suggesting high accuracy of the predicting model. And the results of cross-validation test (q2 =0.8993) and method validation also showed the model of this study exhibited optimum stability and better predictive power than that from semi-empirical method. The model achieved can be used to predict lgKow of congeneric compounds.

  5. Cell-free synthesis of functional human epidermal growth factor receptor: Investigation of ligand-independent dimerization in Sf21 microsomal membranes using non-canonical amino acids

    Science.gov (United States)

    Quast, Robert B.; Ballion, Biljana; Stech, Marlitt; Sonnabend, Andrei; Varga, Balázs R.; Wüstenhagen, Doreen A.; Kele, Péter; Schiller, Stefan M.; Kubick, Stefan

    2016-01-01

    Cell-free protein synthesis systems represent versatile tools for the synthesis and modification of human membrane proteins. In particular, eukaryotic cell-free systems provide a promising platform for their structural and functional characterization. Here, we present the cell-free synthesis of functional human epidermal growth factor receptor and its vIII deletion mutant in a microsome-containing system derived from cultured Sf21 cells. We provide evidence for embedment of cell-free synthesized receptors into microsomal membranes and asparagine-linked glycosylation. Using the cricket paralysis virus internal ribosome entry site and a repetitive synthesis approach enrichment of receptors inside the microsomal fractions was facilitated thereby providing analytical amounts of functional protein. Receptor tyrosine kinase activation was demonstrated by monitoring receptor phosphorylation. Furthermore, an orthogonal cell-free translation system that provides the site-directed incorporation of p-azido-L-phenylalanine is characterized and applied to investigate receptor dimerization in the absence of a ligand by photo-affinity cross-linking. Finally, incorporated azides are used to generate stable covalently linked receptor dimers by strain-promoted cycloaddition using a novel linker system. PMID:27670253

  6. Partitioning Uncertain Workflows

    CERN Document Server

    Huberman, Bernardo A

    2015-01-01

    It is common practice to partition complex workflows into separate channels in order to speed up their completion times. When this is done within a distributed environment, unavoidable fluctuations make individual realizations depart from the expected average gains. We present a method for breaking any complex workflow into several workloads in such a way that once their outputs are joined, their full completion takes less time and exhibit smaller variance than when running in only one channel. We demonstrate the effectiveness of this method in two different scenarios; the optimization of a convex function and the transmission of a large computer file over the Internet.

  7. Three Dimensional Canonical Quantum Gravity

    OpenAIRE

    Matschull, Hans-Juergen

    1995-01-01

    General aspects of vielbein representation, ADM formulation and canonical quantization of gravity are reviewed using pure gravity in three dimensions as a toy model. The classical part focusses on the role of observers in general relativity, which will later be identified with quantum observers. A precise definition of gauge symmetries and a classification of inequivalent solutions of Einstein's equations in dreibein formalism is given as well. In the quantum part the construction of the phys...

  8. CaSR function in the intestine: Hormone secretion, electrolyte absorption and secretion, paracrine non-canonical Wnt signaling and colonic crypt cell proliferation.

    Science.gov (United States)

    Macleod, R John

    2013-06-01

    Expression and function of the CaSR have been shown in some mammalian taste buds and basal cells of the esophagus. Signaling cascades responsible for CaSR-mediated stimulation of H(+)-K(+)-ATPase on human parietal cells have been defined. Transgenic mice and reductionistic cell culture models have shown that the CaSR promotes gastrin secretion from G cells, cholecystokinin (CCK) secretion from duodenal I cells and BMP-2 secretion from sub-epithelial myofibroblasts. In addition, the CaSR mediates a novel paracrine relationship between myofibroblasts and overlying epithelial cells in the colon. Thus, CaSR activators stimulate secretion of Wnt5a from myofibroblasts and expression of the Wnt5a receptor Ror2 in epithelial cells. CaSR-mediated Wnt5a/Ror2 engagement stimulates epithelial differentiation and reduces expression of the receptor for tumor necrosis factor (TNFR1). CaSR activators also modulate intestinal motility, inhibit Cl(-) secretion and stimulate Na(+) absorption in both the small intestine and colon. Colonic epithelia from conditional and global CaSR knockout mice exhibit increased proliferation with increased Wnt/β-catenin signaling, demonstrating that the CaSR negatively modulates colonic epithelial growth.

  9. Classification algorithms using adaptive partitioning

    KAUST Repository

    Binev, Peter

    2014-12-01

    © 2014 Institute of Mathematical Statistics. Algorithms for binary classification based on adaptive tree partitioning are formulated and analyzed for both their risk performance and their friendliness to numerical implementation. The algorithms can be viewed as generating a set approximation to the Bayes set and thus fall into the general category of set estimators. In contrast with the most studied tree-based algorithms, which utilize piecewise constant approximation on the generated partition [IEEE Trans. Inform. Theory 52 (2006) 1335.1353; Mach. Learn. 66 (2007) 209.242], we consider decorated trees, which allow us to derive higher order methods. Convergence rates for these methods are derived in terms the parameter - of margin conditions and a rate s of best approximation of the Bayes set by decorated adaptive partitions. They can also be expressed in terms of the Besov smoothness β of the regression function that governs its approximability by piecewise polynomials on adaptive partition. The execution of the algorithms does not require knowledge of the smoothness or margin conditions. Besov smoothness conditions are weaker than the commonly used Holder conditions, which govern approximation by nonadaptive partitions, and therefore for a given regression function can result in a higher rate of convergence. This in turn mitigates the compatibility conflict between smoothness and margin parameters.

  10. The Stem Cell-Expressed Receptor Lgr5 Possesses Canonical and Functionally Active Molecular Determinants Critical to β-arrestin-2 Recruitment

    Science.gov (United States)

    Snyder, Joshua C.; Rochelle, Lauren K.; Barak, Larry S.; Caron, Marc G.

    2013-01-01

    Lgr5 is a membrane protein related to G protein-coupled receptors (GPCR)s whose expression identifies stem cells in multiple tissues and is strongly correlated with cancer. Despite the recent identification of endogenous ligands for Lgr5, its mode of signaling remains enigmatic. The ability to couple to G proteins and βarrestins are classical molecular behaviors of GPCRs that have yet to be observed for Lgr5. Therefore, the goal of this study was to determine if Lgr5 can engage a classical GPCR behavior and elucidate the molecular determinants of this process. Structural analysis of Lgr5 revealed several motifs consistent with its ability to recruit βarr2. Among them, a “SSS” serine cluster located at amino acid position 873-875 within the C-terminal tail (C-tail), is in a region consistent with other GPCRs that bind βarr2 with high-affinity. To test its functionality, a ligand-independent βarr2 translocation assay was implemented. We show that Lgr5 recruits βarr2 and that the “SSS” amino acids (873-875) are absolutely critical to this process. We also demonstrate that for full efficacy, this cluster requires other Lgr5 C-tail serines that were previously shown to be important for constitutive and βarr2 independent internalization of Lgr5. These data are proof of principle that a classical GPCR behavior can be manifested by Lgr5. The existence of alternative ligands or missing effectors of Lgr5 that scaffold this classical GPCR behavior and the downstream signaling pathways engaged should be considered. Characterizing Lgr5 signaling will be invaluable for assessing its role in tissue maintenance, repair, and disease. PMID:24386388

  11. The stem cell-expressed receptor Lgr5 possesses canonical and functionally active molecular determinants critical to β-arrestin-2 recruitment.

    Directory of Open Access Journals (Sweden)

    Joshua C Snyder

    Full Text Available Lgr5 is a membrane protein related to G protein-coupled receptors (GPCRs whose expression identifies stem cells in multiple tissues and is strongly correlated with cancer. Despite the recent identification of endogenous ligands for Lgr5, its mode of signaling remains enigmatic. The ability to couple to G proteins and βarrestins are classical molecular behaviors of GPCRs that have yet to be observed for Lgr5. Therefore, the goal of this study was to determine if Lgr5 can engage a classical GPCR behavior and elucidate the molecular determinants of this process. Structural analysis of Lgr5 revealed several motifs consistent with its ability to recruit βarr2. Among them, a "SSS" serine cluster located at amino acid position 873-875 within the C-terminal tail (C-tail, is in a region consistent with other GPCRs that bind βarr2 with high-affinity. To test its functionality, a ligand-independent βarr2 translocation assay was implemented. We show that Lgr5 recruits βarr2 and that the "SSS" amino acids (873-875 are absolutely critical to this process. We also demonstrate that for full efficacy, this cluster requires other Lgr5 C-tail serines that were previously shown to be important for constitutive and βarr2 independent internalization of Lgr5. These data are proof of principle that a classical GPCR behavior can be manifested by Lgr5. The existence of alternative ligands or missing effectors of Lgr5 that scaffold this classical GPCR behavior and the downstream signaling pathways engaged should be considered. Characterizing Lgr5 signaling will be invaluable for assessing its role in tissue maintenance, repair, and disease.

  12. Stroke in Canon of Medicine

    Science.gov (United States)

    Alorizi, Seyed Morteza Emami; Nimruzi, Majid

    2016-01-01

    Background: Stroke has a huge negative impact on the society and more adversely affect women. There is scarce evidence about any neuroprotective effects of commonly used drug in acute stroke. Bushnell et al. provided a guideline focusing on the risk factors of stroke unique to women, including reproductive factors, metabolic syndrome, obesity, atrial fibrillation, and migraine with aura. The ten variables cited by Avicenna in Canon of Medicine would compensate for the gaps mentioned in this guideline. The prescribed drugs should be selected qualitatively opposite to Mizaj (warm-cold and wet-dry qualities induced by disease state) of the disease and according to ten variables, including the nature of the affected organ, intensity of disease, sex, age, habit, season, place of living, occupation, stamina and physical status. Methods: Information related to stroke was searched in Canon of Medicine, which is an outstanding book in traditional Persian medicine written by Avicenna. Results: A hemorrhagic stroke is the result of increasing sanguine humor in the body. Sanguine has warm-wet quality, and should be treated with food and drugs that quench the abundance of blood in the body. An acute episode of ischemic stroke is due to the abundance of phlegm that causes a blockage in the cerebral vessels. Phlegm has cold-wet quality and treatment should be started with compound medicines that either solve the phlegm or eject it from the body. Conclusion: Avicenna has cited in Canon of Medicine that women have cold and wet temperament compared to men. For this reason, they are more prone to accumulation of phlegm in their body organs including the liver, joints and vessels, and consequently in the risk of fatty liver, degenerative joint disease, atherosclerosis, and stroke especially the ischemic one. This is in accordance with epidemiological studies that showed higher rate of ischemic stroke in women rather than hemorrhagic one. PMID:26722147

  13. Canonical metrics on complex manifold

    Institute of Scientific and Technical Information of China (English)

    YAU Shing-Tung

    2008-01-01

    @@ Complex manifolds are topological spaces that are covered by coordinate charts where the Coordinate changes are given by holomorphic transformations. For example, Riemann surfaces are one dimensional complex manifolds. In order to understand complex manifolds, it is useful to introduce metrics that are compatible with the complex structure. In general, we should have a pair (M, ds2M) where ds2M is the metric. The metric is said to be canonical if any biholomorphisms of the complex manifolds are automatically isometries. Such metrics can naturally be used to describe invariants of the complex structures of the manifold.

  14. Canonical metrics on complex manifold

    Institute of Scientific and Technical Information of China (English)

    YAU; Shing-Tung(Yau; S.-T.)

    2008-01-01

    Complex manifolds are topological spaces that are covered by coordinate charts where the coordinate changes are given by holomorphic transformations.For example,Riemann surfaces are one dimensional complex manifolds.In order to understand complex manifolds,it is useful to introduce metrics that are compatible with the complex structure.In general,we should have a pair(M,ds~2_M)where ds~2_M is the metric.The metric is said to be canonical if any biholomorphisms of the complex manifolds are automatically isometries.Such metrics can naturally be used to describe invariants of the complex structures of the manifold.

  15. Dibaryons as canonically quantized biskyrmions

    CERN Document Server

    Krupovnickas, T; Riska, D O

    2000-01-01

    The characteristic feature of the ground state configuration of the Skyrme model description of nuclei is the absence of recognizable individual nucleons. The ground state of the skyrmion with baryon number 2 is axially symmetric, and is well approximated by a simple rational map, which represents a direct generalization of Skyrme's hedgehog ansatz for the nucleon. If the Lagrangian density is canonically quantized this configuration may support excitations that lie close and possible below the threshold for pion decay, and therefore describe dibaryons. The quantum corrections stabilize these solutions, the mass density of which have the correct exponential fall off at large distances.

  16. Canonical path integral quantization of Einstein's gravitational field

    OpenAIRE

    Muslih, Sami I.

    2000-01-01

    The connection between the canonical and the path integral formulations of Einstein's gravitational field is discussed using the Hamilton - Jacobi method. Unlike conventional methods, it is shown that our path integral method leads to obtain the measure of integration with no $\\delta$- functions, no need to fix any gauge and so no ambiguous deteminants will appear.

  17. On the Canonical Formalism for a Higher-Curvature Gravity

    CERN Document Server

    Ezawa, Y; Kajihara, M; Soda, J; Yano, T; Ezawa, Yasuo; Kiminami, Masahiko; Kajihara, Masahiro; Soda, Jiro; Yano, Tadasi

    1999-01-01

    Following the method of Buchbinder and Lyahovich, we carry out a canonical formalism for a higher-curvature gravity in which the Lagrangian density ${\\cal L}$ is given in terms of a function of the salar curvature $R$ as ${\\cal L}=\\sqrt{-\\det g_{\\mu\

  18. A parametric study on the buckling of functionally graded material plates with internal discontinuities using the partition of unity method

    OpenAIRE

    S Natarajan; Chakraborty, S.; M. Ganapathi; Subramaniam, M

    2013-01-01

    In this paper, the effect of local defects, viz., cracks and cutouts on the buckling behaviour of functionally graded material plates subjected to mechanical and thermal load is numerically studied. The internal discontinuities, viz., cracks and cutouts are represented independent of the mesh within the framework of the extended finite element method and an enriched shear flexible 4-noded quadrilateral element is used for the spatial discretization. The properties are assumed to vary only in ...

  19. A Canonical Laplacian on the Algebra of Densities on a Projectively Connected Manifold

    OpenAIRE

    George, Jacob

    2009-01-01

    On a manifold with a projective connection we canonically assign a second order differential operator acting on the algebra of all densities to any tensor density $S^{ij}$ of fixed weight $\\lambda$. In particular, this implies that on any projectively connected manifold, a `bracket' (symmetric biderivation) on the algebra of functions extends canonically to the algebra of densities.

  20. Hard-sphere fluids inside spherical, hard pores. Grand canonical ensemble Monte Carlo calculations and integral equation approximations

    DEFF Research Database (Denmark)

    Sloth, Peter

    1990-01-01

    Density profiles and partition coefficients are obtained for hard-sphere fluids inside hard, spherical pores of different sizes by grand canonical ensemble Monte Carlo calculations. The Monte Carlo results are compared to the results obtained by application of different kinds of integral equation...

  1. Integral canonical models for Spin Shimura varieties

    OpenAIRE

    Pera, Keerthi Madapusi

    2012-01-01

    We construct regular integral canonical models for Shimura varieties attached to Spin groups at (possibly ramified) odd primes. We exhibit these models as schemes of 'relative PEL type' over integral canonical models of larger Spin Shimura varieties with good reduction. Work of Vasiu-Zink then shows that the classical Kuga-Satake construction extends over the integral model and that the integral models we construct are canonical in a very precise sense. We also construct good compactification...

  2. Niche partitioning of feeding microhabitats produces a unique function for herbivorous rabbitfishes (Perciformes, Siganidae) on coral reefs

    Science.gov (United States)

    Fox, R. J.; Bellwood, D. R.

    2013-03-01

    Niche theory predicts that coexisting species minimise competition by evolving morphological or behavioural specialisations that allow them to spread out along resource axes such as space, diet and temporal activity. These specialisations define how a species interacts with its environment and, by extension, determine its functional role. Here, we examine the feeding niche of three species of coral reef-dwelling rabbitfishes (Siganidae, Siganus). By comparing aspects of their feeding behaviour (bite location, bite rate, foraging distance) with that of representative species from two other abundant herbivorous fish families, the parrotfishes (Labridae, Scarus) and surgeonfishes (Acanthuridae, Acanthurus), we examine whether rabbitfishes have a feeding niche distinct from other members of the herbivore guild. Measurements of the penetration of the fishes' snouts and bodies into reef concavities when feeding revealed that rabbitfish fed to a greater degree from reef crevices and interstices than other herbivores. There was just a 40 % overlap in the penetration-depth niche between rabbitfish and surgeonfish and a 45 % overlap between rabbitfish and parrotfish, compared with the almost complete niche overlap (95 %) recorded for parrotfish and surgeonfish along this spatial niche axis. Aspects of the morphology of rabbitfish which may contribute to this niche segregation include a comparatively longer, narrower snout and narrower head. Our results suggest that sympatric coexistence of rabbitfish and other reef herbivores is facilitated by segregation along a spatial (and potentially dietary) axis. This segregation results in a unique functional role for rabbitfishes among roving herbivores that of "crevice-browser": a group that specifically feeds on crevice-dwelling algal or benthic organisms. This functional trait may have implications for reef ecosystem processes in terms of controlling the successional development of crevice-based algal communities, reducing their

  3. Controlled levels of canonical Wnt signaling are required for neural crest migration.

    Science.gov (United States)

    Maj, Ewa; Künneke, Lutz; Loresch, Elisabeth; Grund, Anita; Melchert, Juliane; Pieler, Tomas; Aspelmeier, Timo; Borchers, Annette

    2016-09-01

    Canonical Wnt signaling plays a dominant role in the development of the neural crest (NC), a highly migratory cell population that generates a vast array of cell types. Canonical Wnt signaling is required for NC induction as well as differentiation, however its role in NC migration remains largely unknown. Analyzing nuclear localization of β-catenin as readout for canonical Wnt activity, we detect nuclear β-catenin in premigratory but not migratory Xenopus NC cells suggesting that canonical Wnt activity has to decrease to basal levels to enable NC migration. To define a possible function of canonical Wnt signaling in Xenopus NC migration, canonical Wnt signaling was modulated at different time points after NC induction. This was accomplished using either chemical modulators affecting β-catenin stability or inducible glucocorticoid fusion constructs of Lef/Tcf transcription factors. In vivo analysis of NC migration by whole mount in situ hybridization demonstrates that ectopic activation of canonical Wnt signaling inhibits cranial NC migration. Further, NC transplantation experiments confirm that this effect is tissue-autonomous. In addition, live-cell imaging in combination with biophysical data analysis of explanted NC cells confirms the in vivo findings and demonstrates that modulation of canonical Wnt signaling affects the ability of NC cells to perform single cell migration. Thus, our data support the hypothesis that canonical Wnt signaling needs to be tightly controlled to enable migration of NC cells. PMID:27341758

  4. Controlled levels of canonical Wnt signaling are required for neural crest migration.

    Science.gov (United States)

    Maj, Ewa; Künneke, Lutz; Loresch, Elisabeth; Grund, Anita; Melchert, Juliane; Pieler, Tomas; Aspelmeier, Timo; Borchers, Annette

    2016-09-01

    Canonical Wnt signaling plays a dominant role in the development of the neural crest (NC), a highly migratory cell population that generates a vast array of cell types. Canonical Wnt signaling is required for NC induction as well as differentiation, however its role in NC migration remains largely unknown. Analyzing nuclear localization of β-catenin as readout for canonical Wnt activity, we detect nuclear β-catenin in premigratory but not migratory Xenopus NC cells suggesting that canonical Wnt activity has to decrease to basal levels to enable NC migration. To define a possible function of canonical Wnt signaling in Xenopus NC migration, canonical Wnt signaling was modulated at different time points after NC induction. This was accomplished using either chemical modulators affecting β-catenin stability or inducible glucocorticoid fusion constructs of Lef/Tcf transcription factors. In vivo analysis of NC migration by whole mount in situ hybridization demonstrates that ectopic activation of canonical Wnt signaling inhibits cranial NC migration. Further, NC transplantation experiments confirm that this effect is tissue-autonomous. In addition, live-cell imaging in combination with biophysical data analysis of explanted NC cells confirms the in vivo findings and demonstrates that modulation of canonical Wnt signaling affects the ability of NC cells to perform single cell migration. Thus, our data support the hypothesis that canonical Wnt signaling needs to be tightly controlled to enable migration of NC cells.

  5. El canon de la periferia

    Directory of Open Access Journals (Sweden)

    Karina Beatriz Lemes

    2010-11-01

    Full Text Available Intentaremos mostrar cómo venimos trabajando con la reconstrucción de la memoria literaria de la provincia de Misiones a partir de la recopilación de los manuscritos de sus autores más representativos. Hemos utilizado para nuestra lectura, en cruce con la crítica genética, las relaciones que Fernando Ainsa establece entre canon y periferia,  espacios de la memoria y construcción de la utopía. Ainsa concibe la escritura como proceso genético que en su origen es personal, visceral y solitario, una búsqueda constante de identidad que se enriquece en contacto con el mundo, con la apertura de fronteras. Estas vinculaciones nos han permitido interpretar las prácticas sociales que fundaron actividades estéticas en la distancia de los centros de poder argentinos.This paper shows some findings of our ongoing research project dealing with the recuperation of literary memory in the province of Misiones by analysing a compilation of the literary manuscripts by the most representative authors of this northern region of Argentina. Here, we follow Fernado Ainsa’s notions of canon and periphery, of memory spaces and construction of utopias. Ainsa sees the act of writing as a genetic process for it originates within a personal, visceral, and solitary realm. For Ainsa, writing is also a permanent search for identity which becomes richer when in contact with the world, when frontiers open up. These concepts allow us to interpret the social practices that gave birth to these aesthetic projects far away from Argentina’s power centers.

  6. [The role of functional status and recursive partition analysis (RPA) classes for the choice of fractionation regimen in patients with high-grade gliomas].

    Science.gov (United States)

    Izmaĭlov, T R; Pan'shin, G A; Datsenko, P V

    2012-01-01

    The treatment results of 396 patients with morphologically verified grade 3-4 malignant brain tumors receiving conventional irradiation regimen and irradiation by medium-sized fractions were analyzed to form institutional guidelines.The standard mode of fractionation with a single dose of 2 Gy and total focal dose (TFD) of 60 Gy is appropriate for patients with initial Karnofsky status of 60-100% and Recursive Partition Analysis (RPA) class I-III. TFD increase to 60-62 Gy in grade 4 gliomas and 54-56 Gy in grade 3 gliomas grants a significant improve in overall survival. An increase of a single irradiation fraction to 3 Gy may be used for patients with initially low functional status (Karnofsky 30-50%) and RPA classes IV-VI. In these cases it is advisable to use the TFD of 45 Gy or more (TFD of equivalent regimen with a dose greater than 54 Gy). The mentioned fractionation regimens could be recommended for the use in clinical practice to improve the results of high-grade gliomas treatment. PMID:22888653

  7. Synchrotron Micro-XANES Measurements of Vanadium Oxidation State in Glasses as a Function of Oxygen Fugacity: Experimental Calibration of Data Relevant to Partition Coefficient Determination

    Science.gov (United States)

    Delaney, J. S.; Sutton, S. R.; Newville, M.; Jones, J. H.; Hanson, B.; Dyar, M. D.; Schreiber, H.

    2000-01-01

    Oxidation state microanalyses for V in glass have been made by calibrating XANES spectral features with optical spectroscopic measurements. The oxidation state change with fugacity of O2 will strongly influence partitioning results.

  8. Regenerative partition structures

    OpenAIRE

    Gnedin, Alexander; Pitman, Jim

    2004-01-01

    We consider Kingman's partition structures which are regenerative with respect to a general operation of random deletion of some part. Prototypes of this class are the Ewens partition structures which Kingman characterised by regeneration after deletion of a part chosen by size-biased sampling. We associate each regenerative partition structure with a corresponding regenerative composition structure, which (as we showed in a previous paper) can be associated in turn with a regenerative random...

  9. Plasmid and chromosome partitioning: surprises from phylogeny

    DEFF Research Database (Denmark)

    Gerdes, Kenn; Møller-Jensen, Jakob; Bugge Jensen, Rasmus

    2000-01-01

    and chromosomes from prokaryotic organisms. All known plasmid-encoded par loci specify three components: a cis-acting centromere-like site and two trans-acting proteins that form a nucleoprotein complex at the centromere (i.e. the partition complex). The proteins are encoded by two genes in an operon...... that is autoregulated by the par-encoded proteins. In all cases, the upstream gene encodes an ATPase that is essential for partitioning. Recent cytological analyses indicate that the ATPases function as adaptors between a host-encoded component and the partition complex and thereby tether plasmids and chromosomal...... origin regions to specific subcellular sites (i.e. the poles or quarter-cell positions). Two types of partitioning ATPases are known: the Walker-type ATPases encoded by the par/sop gene family (type I partitioning loci) and the actin-like ATPase encoded by the par locus of plasmid R1 (type II...

  10. Discussion on Forest Land Functional Partition and Discrepant Protection and Utilization in Tibet%西藏林地功能分区及差别化保护利用探讨

    Institute of Scientific and Technical Information of China (English)

    范志浩; 姜灿荣

    2012-01-01

    根据西藏的自然环境条件,结合林地保护管理现状,将全区林地划分为4个功能区,并就各区域林地的功能定位、差别化保护利用以及相应的管理措施进行探讨。%According to the natural environment, combining with forest land protection and management situa- tion ,Tibet was classified as four forest lands functional partition. In this paper, it discussed forest land function orientation, discrepant protection and utilization and appropriate management measures for each forest lands functional partition

  11. A single NFκB system for both canonical and non-canonical signaling

    Institute of Scientific and Technical Information of China (English)

    Vincent Feng-Sheng Shih; Rachel Tsui; Andrew Caldwell; Alexander Hoffmann

    2011-01-01

    Two distinct nuclear factor κB(NFκB)signaling pathways have been described; the canonical pathway that mediates inflammatory responses,and the non-canonical pathway that is involved in immune cell differentiation and maturation and secondary lymphoid organogenesis.The former is dependent on the IκB kinase adaptor molecule NEMO,the latter is independent of it.Here,we review the molecular mechanisms of regulation in each signaling axis and attempt to relate the apparent regulatory logic to the physiological function.Further,we review the recent evidence for extensive cross-regulation between these two signaling axes and summarize them in a wiring diagram.These observations suggest that NEMO-dependent and-independent signaling should be viewed within the context of a single NFκB signaling system,which mediates signaling from both inflammatory and organogenic stimuli in an integrated manner.As in other regulatory biological systems,a systems approach including mathematical models that include quantitative and kinetic information will be necessary to characterize the network properties that mediate physiological function,and that may break down to cause or contribute to pathology.

  12. De canon : een oude katholieke kerkstructuur?

    NARCIS (Netherlands)

    Smit, P.B.A.

    2011-01-01

    Op 30 november 2011 houdt theoloog prof. dr. Peter-Ben Smit zijn oratie aan de Universiteit Utrecht. Daarin gaat hij na hoe de canon van het Nieuwe Testament tot stand kwam binnen de vroege kerk, en wat de functie van de canon was bij de uitleg - oftewel exegese - van de Schrift. Dit onderwerp kwam

  13. CANONICAL EXTENSIONS OF SYMMETRIC LINEAR RELATIONS

    NARCIS (Netherlands)

    Sandovici, Adrian; Davidson, KR; Gaspar, D; Stratila, S; Timotin, D; Vasilescu, FH

    2006-01-01

    The concept of canonical extension of Hermitian operators has been recently introduced by A. Kuzhel. This paper deals with a generalization of this notion to the case of symmetric linear relations. Namely, canonical regular extensions of symmetric linear relations in Hilbert spaces are studied. The

  14. The Current Canon in British Romantics Studies.

    Science.gov (United States)

    Linkin, Harriet Kramer

    1991-01-01

    Describes and reports on a survey of 164 U.S. universities to ascertain what is taught as the current canon of British Romantic literature. Asserts that the canon may now include Mary Shelley with the former standard six major male Romantic poets, indicating a significant emergence of a feminist perspective on British Romanticism in the classroom.…

  15. Canon, Jubilees 23 and Psalm 90

    Directory of Open Access Journals (Sweden)

    Pieter M. Venter

    2014-02-01

    Full Text Available There never existed only one form of the biblical canon. This can be seen in the versions as well as editions of the Hebrew and Greek Bibles. History and circumstances played a central role in the gradual growth of eventually different forms of the biblical canon. This process can be studied using the discipline of intertextuality. There always was a movement from traditum to traditio in the growth of these variant forms of biblical canon. This can be seen in an analysis of the intertextuality in Jubilees 23:8–32. The available canon of the day was interpreted there, not according to a specific demarcated volume of canonical scriptures, but in line with the theology presented in those materials, especially that of Psalm 90.

  16. Incompatibility boundaries for properties of community partitions

    CERN Document Server

    Browet, Arnaud; Sarlette, Alain

    2016-01-01

    We prove the incompatibility of certain desirable properties of community partition quality functions. Our results generalize the impossibility result of [Kleinberg 2003] by considering sets of weaker properties. In particular, we use an alternative notion to solve the central issue of the consistency property. (The latter means that modifying the graph in a way consistent with a partition should not have counterintuitive effects). Our results clearly show that community partition methods should not be expected to perfectly satisfy all ideally desired properties. We then proceed to show that this incompatibility no longer holds when slightly relaxed versions of the properties are considered, and we provide in fact examples of simple quality functions satisfying these relaxed properties. An experimental study of these quality functions shows a behavior comparable to established methods in some situations, but more debatable results in others. This suggests that defining a notion of good partition in communitie...

  17. Improved models for the prediction of activity coefficients in nearly athermal mixtures .2. A theoretically-based G(E)-model based on the van der Waals partition function

    DEFF Research Database (Denmark)

    Kontogeorgis, Georgios; Georgios, Nikolopoulos; Fredenslund, Aage;

    1997-01-01

    of the generalized van der Waals partition function and attempts to account for all non-energetic effects of solutions of both short- and long-chain alkanes, including alkane polymers. Both the free-volume effects and the density-dependent rotational degrees of freedom are considered. The resulting G(E)-model which......, despite its derivation from a partition function resembles the Flory-Huggins formula, is suitable for vapor-liquid and solid-liquid equilibrium calculations for nearly athermal polymer solutions as well as for alkane systems. We show that using plausible assumptions for the free-volume and the external......-degree-of-freedom parameter, very good predictions are obtained for activity coefficients of asymmetric alkane systems at both concentration ends, for solid-liquid equilibrium calculations, as well as in extreme cases (polymer solutions, activity coefficients of heavy model alkane polymers in short-chain compounds recently...

  18. Self-consistent thermodynamics for the Tsallis statistics in the grand canonical ensemble: Nonrelativistic hadron gas

    Energy Technology Data Exchange (ETDEWEB)

    Parvan, A.S. [Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics, Dubna (Russian Federation); Horia Hulubei National Institute of Physics and Nuclear Engineering, Department of Theoretical Physics, Bucharest (Romania); Moldova Academy of Sciences, Institute of Applied Physics, Chisinau (Moldova, Republic of)

    2015-09-15

    In the present paper, the Tsallis statistics in the grand canonical ensemble was reconsidered in a general form. The thermodynamic properties of the nonrelativistic ideal gas of hadrons in the grand canonical ensemble was studied numerically and analytically in a finite volume and the thermodynamic limit. It was proved that the Tsallis statistics in the grand canonical ensemble satisfies the requirements of the equilibrium thermodynamics in the thermodynamic limit if the thermodynamic potential is a homogeneous function of the first order with respect to the extensive variables of state of the system and the entropic variable z = 1/(q - 1) is an extensive variable of state. The equivalence of canonical, microcanonical and grand canonical ensembles for the nonrelativistic ideal gas of hadrons was demonstrated. (orig.)

  19. On the relationship between the modifications to the Raychaudhuri equation and the canonical Hamiltonian structures

    CERN Document Server

    Singh, Parampreet

    2015-01-01

    The problem of obtaining canonical Hamiltonian structures from the equations of motion is studied in the context of the spatially flat Friedmann-Robertson-Walker models. Modifications to Raychaudhuri equation are implemented independently as quadratic and cubic terms of energy density without introducing additional degrees of freedom. Depending on its sign, modifications make gravity repulsive above a curvature scale for matter satisfying strong energy condition, or more attractive than in the classical theory. Canonical structure of the modified theories is determined demanding that the total Hamiltonian be a linear combination of gravity and matter Hamiltonians. Both of the repulsive modifications are found to yield singularity avoidance. In the quadratic repulsive case, the modified canonical phase space of gravity is a polymerized phase space with canonical momentum as inverse trigonometric function of Hubble rate; the canonical Hamiltonian can be identified with the effective Hamiltonian in loop quantum ...

  20. On the relationship between modifications to the Raychaudhuri equation and the canonical Hamiltonian structures

    Science.gov (United States)

    Singh, Parampreet; Soni, S. K.

    2016-06-01

    The problem of obtaining canonical Hamiltonian structures from the equations of motion, without any knowledge of the action, is studied in the context of the spatially flat Friedmann, ‘Robertson’, and Walker models. Modifications to the Raychaudhuri equation are implemented independently as quadratic and cubic terms of energy density without introducing additional degrees of freedom. Depending on their sign, modifications make gravity repulsive above a curvature scale for matter satisfying strong energy conditions, or more attractive than in the classical theory. The canonical structure of the modified theories is determined by demanding that the total Hamiltonian be a linear combination of gravity and matter Hamiltonians. In the quadratic repulsive case, the modified canonical phase space of gravity is a polymerized phase space with canonical momentum as inverse a trigonometric function of the Hubble rate; the canonical Hamiltonian can be identified with the effective Hamiltonian in loop quantum cosmology. The repulsive cubic modification results in a ‘generalized polymerized’ canonical phase space. Both the repulsive modifications are found to yield singularity avoidance. In contrast, the quadratic and cubic attractive modifications result in a canonical phase space in which canonical momentum is nontrigonometric and singularities persist. Our results hint at connections between the repulsive/attractive nature of modifications to gravity arising from the gravitational sector and polymerized/non polymerized gravitational phase space.

  1. The canonical form of the Rabi hamiltonian

    CERN Document Server

    Szopa, M; Ceulemans, A; Szopa, Marek; Mys, Geert; Ceulemans, Arnout

    1996-01-01

    The Rabi Hamiltonian, describing the coupling of a two-level system to a single quantized boson mode, is studied in the Bargmann-Fock representation. The corresponding system of differential equations is transformed into a canonical form in which all regular singularities between zero and infinity have been removed. The canonical or Birkhoff-transformed equations give rise to a two-dimensional eigenvalue problem, involving the energy and a transformational parameter which affects the coupling strength. The known isolated exact solutions of the Rabi Hamiltonian are found to correspond to the uncoupled form of the canonical system.

  2. Thinning Invariant Partition Structures

    CERN Document Server

    Starr, Shannon

    2011-01-01

    A partition structure is a random point process on $[0,1]$ whose points sum to 1, almost surely. In the case that there are infinitely many points to begin with, we consider a thinning action by: first, removing points independently, such that each point survives with probability $p>0$; and, secondly, rescaling the remaining points by an overall factor to normalize the sum again to 1. We prove that the partition structures which are "thinning divisible" for a sequence of $p$'s converging to 0 are mixtures of the Poisson-Kingman partition structures. We also consider the property of being "thinning invariant" for all $p \\in (0,1)$.

  3. The Literary Canon in the Age of New Media

    DEFF Research Database (Denmark)

    Backe, Hans-Joachim

    2015-01-01

    The article offers a comparative overview of the diverging courses of the canon debate in Anglophone and Germanophone contexts. While the Anglophone canon debate has focused on the politics of canon composition, the Germanophone canon debate has been more concerned with the malleability and media......The article offers a comparative overview of the diverging courses of the canon debate in Anglophone and Germanophone contexts. While the Anglophone canon debate has focused on the politics of canon composition, the Germanophone canon debate has been more concerned with the malleability...

  4. The canonical Kravchuk basis for discrete quantum mechanics

    Science.gov (United States)

    Hakioglu, Tugrul; Wolf, Kurt Bernardo

    2000-04-01

    The well known Kravchuk formalism of the harmonic oscillator obtained from the direct discretization method is shown to be a new way of formulating discrete quantum phase space. It is shown that the Kravchuk oscillator Hamiltonian has a well defined unitary canonical partner which we identify with the quantum phase of the Kravchuk oscillator. The generalized discrete Wigner function formalism based on the action and angle variables is applied to the Kravchuk oscillator and its continuous limit is examined.

  5. Regularized canonical correlation analysis with unlabeled data

    Institute of Scientific and Technical Information of China (English)

    Xi-chuan ZHOU; Hai-bin SHEN

    2009-01-01

    In standard canonical correlation analysis (CCA), the data from definite datasets are used to estimate their canonical correlation. In real applications, for example in bilingual text retrieval, it may have a great portion of data that we do not know which set it belongs to. This part of data is called unlabeled data, while the rest from definite datasets is called labeled data. We propose a novel method called regularized canonical correlation analysis (RCCA), which makes use of both labeled and unlabeled samples. Specifically, we learn to approximate canonical correlation as if all data were labeled. Then. we describe a generalization of RCCA for the multi-set situation. Experiments on four real world datasets, Yeast, Cloud, Iris, and Haberman, demonstrate that,by incorporating the unlabeled data points, the accuracy of correlation coefficients can be improved by over 30%.

  6. Canonical equations of Hamilton with beautiful symmetry

    OpenAIRE

    Liang, Guo; Guo, Qi

    2012-01-01

    The Hamiltonian formulation plays the essential role in constructing the framework of modern physics. In this paper, a new form of canonical equations of Hamilton with the complete symmetry is obtained, which are valid not only for the first-order differential system, but also for the second-order differential system. The conventional form of the canonical equations without the symmetry [Goldstein et al., Classical Mechanics, 3rd ed, Addison-Wesley, 2001] are only for the second-order differe...

  7. Carbon partitioning in photosynthesis.

    Science.gov (United States)

    Melis, Anastasios

    2013-06-01

    The work seeks to raise awareness of a fundamental problem that impacts the renewable generation of fuels and chemicals via (photo)synthetic biology. At issue is regulation of the endogenous cellular carbon partitioning between different biosynthetic pathways, over which the living cell exerts stringent control. The regulation of carbon partitioning in photosynthesis is not understood. In plants, microalgae and cyanobacteria, methods need be devised to alter photosynthetic carbon partitioning between the sugar, terpenoid, and fatty acid biosynthetic pathways, to lower the prevalence of sugar biosynthesis and correspondingly upregulate terpenoid and fatty acid hydrocarbons production in the cell. Insight from unusual but naturally occurring carbon-partitioning processes can help in the design of blueprints for improved photosynthetic fuels and chemicals production.

  8. Refining inflation using non-canonical scalars

    Energy Technology Data Exchange (ETDEWEB)

    Unnikrishnan, Sanil; Sahni, Varun [Inter-University Centre for Astronomy and Astrophysics, Post Bag 4, Ganeshkhind, Pune 411 007 (India); Toporensky, Aleksey, E-mail: sanil@iucaa.ernet.in, E-mail: varun@iucaa.ernet.in, E-mail: atopor@rambler.ru [Sternberg Astronomical Institute, Moscow State University, Universitetsky Prospekt, 13, Moscow 119992 (Russian Federation)

    2012-08-01

    This paper revisits the Inflationary scenario within the framework of scalar field models possessing a non-canonical kinetic term. We obtain closed form solutions for all essential quantities associated with chaotic inflation including slow roll parameters, scalar and tensor power spectra, spectral indices, the tensor-to-scalar ratio, etc. We also examine the Hamilton-Jacobi equation and demonstrate the existence of an inflationary attractor. Our results highlight the fact that non-canonical scalars can significantly improve the viability of inflationary models. They accomplish this by decreasing the tensor-to-scalar ratio while simultaneously increasing the value of the scalar spectral index, thereby redeeming models which are incompatible with the cosmic microwave background (CMB) in their canonical version. For instance, the non-canonical version of the chaotic inflationary potential, V(φ) ∼ λφ{sup 4}, is found to agree with observations for values of λ as large as unity! The exponential potential can also provide a reasonable fit to CMB observations. A central result of this paper is that steep potentials (such as V∝φ{sup −n}) usually associated with dark energy, can drive inflation in the non-canonical setting. Interestingly, non-canonical scalars violate the consistency relation r = −8n{sub T}, which emerges as a smoking gun test for this class of models.

  9. Both canonical and non-canonical Wnt signaling independently promote stem cell growth in mammospheres.

    Directory of Open Access Journals (Sweden)

    Alexander M Many

    Full Text Available The characterization of mammary stem cells, and signals that regulate their behavior, is of central importance in understanding developmental changes in the mammary gland and possibly for targeting stem-like cells in breast cancer. The canonical Wnt/β-catenin pathway is a signaling mechanism associated with maintenance of self-renewing stem cells in many tissues, including mammary epithelium, and can be oncogenic when deregulated. Wnt1 and Wnt3a are examples of ligands that activate the canonical pathway. Other Wnt ligands, such as Wnt5a, typically signal via non-canonical, β-catenin-independent, pathways that in some cases can antagonize canonical signaling. Since the role of non-canonical Wnt signaling in stem cell regulation is not well characterized, we set out to investigate this using mammosphere formation assays that reflect and quantify stem cell properties. Ex vivo mammosphere cultures were established from both wild-type and Wnt1 transgenic mice and were analyzed in response to manipulation of both canonical and non-canonical Wnt signaling. An increased level of mammosphere formation was observed in cultures derived from MMTV-Wnt1 versus wild-type animals, and this was blocked by treatment with Dkk1, a selective inhibitor of canonical Wnt signaling. Consistent with this, we found that a single dose of recombinant Wnt3a was sufficient to increase mammosphere formation in wild-type cultures. Surprisingly, we found that Wnt5a also increased mammosphere formation in these assays. We confirmed that this was not caused by an increase in canonical Wnt/β-catenin signaling but was instead mediated by non-canonical Wnt signals requiring the receptor tyrosine kinase Ror2 and activity of the Jun N-terminal kinase, JNK. We conclude that both canonical and non-canonical Wnt signals have positive effects promoting stem cell activity in mammosphere assays and that they do so via independent signaling mechanisms.

  10. Poisson-Kingman partitions

    OpenAIRE

    Pitman, Jim

    2002-01-01

    This paper presents some general formulas for random partitions of a finite set derived by Kingman's model of random sampling from an interval partition generated by subintervals whose lengths are the points of a Poisson point process. These lengths can be also interpreted as the jumps of a subordinator, that is an increasing process with stationary independent increments. Examples include the two-parameter family of Poisson-Dirichlet models derived from the Poisson process of jumps of a stab...

  11. Canonical Coordinates for Retino-Cortical Magnification

    Directory of Open Access Journals (Sweden)

    Luc Florack

    2014-02-01

    Full Text Available A geometric model for a biologically-inspired visual front-end is proposed, based on an isotropic, scale-invariant two-form field. The model incorporates a foveal property typical of biological visual systems, with an approximately linear decrease of resolution as a function of eccentricity, and by a physical size constant that measures the radius of the geometric foveola, the central region characterized by maximal resolving power. It admits a description in singularity-free canonical coordinates generalizing the familiar log-polar coordinates and reducing to these in the asymptotic case of negligibly-sized geometric foveola or, equivalently, at peripheral locations in the visual field. It has predictive power to the extent that quantitative geometric relationships pertaining to retino-cortical magnification along the primary visual pathway, such as receptive field size distribution and spatial arrangement in retina and striate cortex, can be deduced in a principled manner. The biological plausibility of the model is demonstrated by comparison with known facts of human vision.

  12. Canonical quantization of gravity without 'frozen formalism'

    International Nuclear Information System (INIS)

    We write down a quantum gravity equation which generalizes the Wheeler-DeWitt one in view of including a time dependence in the wave functional. The obtained equation provides a consistent canonical quantization of the 3-geometries resulting from a 'gauge-fixing' (3+1)-slicing of the space-time. Our leading idea relies on a criticism to the possibility that, in a quantum space-time, the notion of a (3+1)-slicing formalism (underlying the Wheeler-DeWitt approach) has yet a precise physical meaning. As solution to this problem we propose of adding to the gravity-matter action the so-called kinematical action (indeed in its reduced form, as implemented in the quantum regime), and then we impose the new quantum constraints. As consequence of this revised approach, the quantization procedure of the 3-geometries takes place in a fixed reference frame and the wave functional acquires a time evolution along a one-parameter family of spatial hypersurfaces filling the space-time. We show how the states of the new quantum dynamics can be arranged into an Hilbert space, whose associated inner product induces a conserved probability notion for the 3-geometries. Finally, since the constraints we quantize violate the classical symmetries (i.e., the vanishing nature of the super-Hamiltonian), then a key result is to find a (non-physical) restriction on the initial wave functional phase, ensuring that general relativity outcomes when taking the appropriate classical limit. However, we propose a physical interpretation of the kinematical variables which, based on the analogy with the so-called Gaussian reference fluid, makes allowance even for such classical symmetry violation

  13. A Family of Trigonometrically-fitted Partitioned Runge-Kutta Symplectic Methods

    International Nuclear Information System (INIS)

    We are presenting a family of trigonometrically fitted partitioned Runge-Kutta symplectic methods of fourth order with six stages. The solution of the one dimensional time independent Schroedinger equation is considered by trigonometrically fitted symplectic integrators. The Schroedinger equation is first transformed into a Hamiltonian canonical equation. Numerical results are obtained for the one-dimensional harmonic oscillator and the exponential potential

  14. Covariant Gauge Fixing and Canonical Quantization

    CERN Document Server

    McKeon, D G C

    2011-01-01

    Theories that contain first class constraints possess gauge invariance which results in the necessity of altering the measure in the associated quantum mechanical path integral. If the path integral is derived from the canonical structure of the theory, then the choice of gauge conditions used in constructing Faddeev's measure cannot be covariant. This shortcoming is normally overcome either by using the "Faddeev-Popov" quantization procedure, or by the approach of Batalin-Fradkin-Fradkina-Vilkovisky, and then demonstrating that these approaches are equivalent to the path integral constructed from the canonical approach with Faddeev's measure. We propose in this paper an alternate way of defining the measure for the path integral when it is constructed using the canonical procedure for theories containing first class constraints and that this new approach can be used in conjunction with covariant gauges. This procedure follows the Faddeev-Popov approach, but rather than working with the form of the gauge tran...

  15. A Canonical Analysis of the Massless Superparticle

    CERN Document Server

    McKeon, D G C

    2012-01-01

    The canonical structure of the action for a massless superparticle is considered in d = 2 + 1 and d = 3 + 1 dimensions. This is done by examining the contribution to the action of each of the components of the spinor {\\theta} present; no attempt is made to maintain manifest covariance. Upon using the Dirac Bracket to eliminate the second class constraints arising from the canonical momenta associated with half of these components, we find that the remaining components have canonical momenta that are all first class constraints. From these first class constraints, it is possible to derive the generator of half of the local Fermionic {\\kappa}-symmetry of Siegel; which half is contingent upon the choice of which half of the momenta associated with the components of {\\theta} are taken to be second class constraints. The algebra of the generator of this Fermionic symmetry transformation is examined.

  16. Universal canonical entropy for gravitating systems

    Indian Academy of Sciences (India)

    Ashok Chatterjee; Parthasarathi Majumdar

    2004-10-01

    The thermodynamics of general relativistic systems with boundary, obeying a Hamiltonian constraint in the bulk, is determined solely by the boundary quantum dynamics, and hence by the area spectrum. Assuming, for large area of the boundary, (a) an area spectrum as determined by non-perturbative canonical quantum general relativity (NCQGR), (b) an energy spectrum that bears a power law relation to the area spectrum, (c) an area law for the leading order microcanonical entropy, leading thermal fluctuation corrections to the canonical entropy are shown to be logarithmic in area with a universal coefficient. Since the microcanonical entropy also has universal logarithmic corrections to the area law (from quantum space-time fluctuations, as found earlier) the canonical entropy then has a universal form including logarithmic corrections to the area law. This form is shown to be independent of the index appearing in assumption (b). The index, however, is crucial in ascertaining the domain of validity of our approach based on thermal equilibrium.

  17. A canonical theory of dynamic decision-making

    Directory of Open Access Journals (Sweden)

    John eFox

    2013-04-01

    Full Text Available Decision-making behaviour is studied in many very different fields, from medicine and economics to psychology and neuroscience, with major contributions from mathematics and statistics, computer science, AI and other technical disciplines. However the conceptualisation of what decision-making is and methods for studying it vary greatly and this has resulted in fragmentation of the field. A theory that can accommodate various perspectives may facilitate interdisciplinary working. We present such a theory in which decision-making is articulated as a set of canonical functions that are sufficiently general to accommodate diverse viewpoints, yet sufficiently precise that they can be instantiated in different ways for specific theoretical or practical purposes. The canons cover the whole decision cycle, from the framing of a decision based on the goals, beliefs, and background knowledge of the decision maker to the formulation of decision options, establishing preferences over them, and making commitments. Commitments can lead to the initiation of new decisions and any step in the cycle can incorporate reasoning about previous decisions and the rationales for them, and lead to revising or abandoning existing commitments. The theory situates decision making with respect to other high-level cognitive capabilities like problem-solving, planning and collaborative decision-making. The canonical approach is assessed in three domains: cognitive and neuro-psychology, artificial intelligence, and decision engineering.

  18. Evidence of non-canonical NOTCH signaling

    DEFF Research Database (Denmark)

    Traustadóttir, Gunnhildur Ásta; Jensen, Charlotte H; Thomassen, Mads;

    2016-01-01

    suggested to interact with NOTCH1 and act as an antagonist. This non-canonical interaction is, however controversial, and evidence for a direct interaction, still lacking in mammals. In this study, we elucidated the putative DLK1-NOTCH1 interaction in a mammalian context. Taking a global approach and using...... this interaction to occur between EGF domains 5 and 6 of DLK1 and EGF domains 10-15 of NOTCH1. Thus, our data provide the first evidence for a direct interaction between DLK1 and NOTCH1 in mammals, and substantiate that non-canonical NOTCH ligands exist, adding to the complexity of NOTCH signaling....

  19. Jordan Canonical Form Theory and Practice

    CERN Document Server

    Weintraub, Steven H

    2009-01-01

    Jordan Canonical Form (JCF) is one of the most important, and useful, concepts in linear algebra. The JCF of a linear transformation, or of a matrix, encodes all of the structural information about that linear transformation, or matrix. This book is a careful development of JCF. After beginning with background material, we introduce Jordan Canonical Form and related notions: eigenvalues, (generalized) eigenvectors, and the characteristic and minimum polynomials. We decide the question of diagonalizability, and prove the Cayley-Hamilton theorem. Then we present a careful and complete proof of t

  20. Canonical analysis based on mutual information

    DEFF Research Database (Denmark)

    Nielsen, Allan Aasbjerg; Vestergaard, Jacob Schack

    2015-01-01

    combinations with the information theoretical measure mutual information (MI). We term this type of analysis canonical information analysis (CIA). MI allows for the actual joint distribution of the variables involved and not just second order statistics. While CCA is ideal for Gaussian data, CIA facilitates......Canonical correlation analysis (CCA) is an established multi-variate statistical method for finding similarities between linear combinations of (normally two) sets of multivariate observations. In this contribution we replace (linear) correlation as the measure of association between the linear...

  1. The use and origin of the (Old and New Testament as Christianity’s canon

    Directory of Open Access Journals (Sweden)

    Andries G. van Aarde

    2012-01-01

    Full Text Available This article explained the valuation of Christian believers with regard to the Christian Bible a ‘Holy Scripture’. In the article the notion ‘Scriptural authority’ was connected with an understanding of both the origin and use of the Christian canon. The article described the origin of the Bible in light of the supposition that the Bible functions as (1 book of theology, as well as (2 book of believers and as (3 book of the church. The article consisted of references to the role of the Old Testament and the New Testament canonical collections and the role of ecclesial synodal decisions. It also obtained a graphical overview of the history and dates of the New Testament writings as a canonical list. The article concluded with a reflection on the relevance for the use and authority of the Bible, seen from the perspective of the use and origin of the Bible as Christianity’s canon.

  2. A field theory approach to the evolution of canonical helicity and energy

    CERN Document Server

    You, Setthivoine

    2016-01-01

    A redefinition of the Lagrangian of a multi-particle system in fields reformulates the single-particle, kinetic, and fluid equations governing fluid and plasma dynamics as a single set of generalized Maxwell's equations and Ohm's law for canonical force-fields. The Lagrangian includes new terms representing the coupling between the motion of particle distributions, between distributions and electromagnetic fields, with relativistic contributions. The formulation shows that the concepts of self-organization and canonical helicity transport are applicable across single-particle, kinetic, and fluid regimes, at classical and relativistic scales. The theory gives the basis for comparing canonical helicity change to energy change in general systems. For example, in a fixed, isolated system subject to non-conservative forces, a species' canonical helicity changes less than total energy only if gradients in density or distribution function are shallow.

  3. A field theory approach to the evolution of canonical helicity and energy

    Science.gov (United States)

    You, S.

    2016-07-01

    A redefinition of the Lagrangian of a multi-particle system in fields reformulates the single-particle, kinetic, and fluid equations governing fluid and plasma dynamics as a single set of generalized Maxwell's equations and Ohm's law for canonical force-fields. The Lagrangian includes new terms representing the coupling between the motion of particle distributions, between distributions and electromagnetic fields, with relativistic contributions. The formulation shows that the concepts of self-organization and canonical helicity transport are applicable across single-particle, kinetic, and fluid regimes, at classical and relativistic scales. The theory gives the basis for comparing canonical helicity change to energy change in general systems. For example, in a fixed, isolated system subject to non-conservative forces, a species' canonical helicity changes less than total energy only if gradients in density or distribution function are shallow.

  4. Generating Primes Using Partitions

    OpenAIRE

    Pittu, Ganesh Reddy

    2015-01-01

    This paper presents a new technique of generating large prime numbers using a smaller one by employing Goldbach partitions. Experiments are presented showing how this method produces candidate prime numbers that are subsequently tested using either Miller Rabin or AKS primality tests.

  5. A new method for counting trees with vertex partition

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    A direct and elementary method is provided in this paper for counting trees with vertex partition instead of recursion, generating function, functional equation, Lagrange inversion, and matrix methods used before.

  6. Regularized Multiple-Set Canonical Correlation Analysis

    Science.gov (United States)

    Takane, Yoshio; Hwang, Heungsun; Abdi, Herve

    2008-01-01

    Multiple-set canonical correlation analysis (Generalized CANO or GCANO for short) is an important technique because it subsumes a number of interesting multivariate data analysis techniques as special cases. More recently, it has also been recognized as an important technique for integrating information from multiple sources. In this paper, we…

  7. Part and Bipartial Canonical Correlation Analysis.

    Science.gov (United States)

    Timm, Neil H.; Carlson, James E.

    Part and bi-partial canonical correlations were developed by extending the definitions of part and bi-partial correlation to sets of variates. These coefficients may be used to help researchers explore relationships which exist among several sets of normally distributed variates. (Author)

  8. Kelvin's Canonical Circulation Theorem in Hall Magnetohydrodynamics

    CERN Document Server

    Shivamoggi, B K

    2016-01-01

    The purpose of this paper is to show that, thanks to the restoration of the legitimate connection between the current density and the plasma flow velocity in Hall magnetohydrodynamics (MHD), Kelvin's Circulation Theorem becomes valid in Hall MHD. The ion-flow velocity in the usual circulation integral is now replaced by the canonical ion-flow velocity.

  9. Canonical transformation method in classical electrodynamics

    Science.gov (United States)

    Pavlenko, Yu. G.

    1983-08-01

    The solutions of Maxwell's equations in the parabolic equation approximation is obtained on the basis of the canonical transformation method. The Hamiltonian form of the equations for the field in an anisotropic stratified medium is also examined. The perturbation theory for the calculation of the wave reflection and transmission coefficients is developed.

  10. Canonical Transformation to the Free Particle

    Science.gov (United States)

    Glass, E. N.; Scanio, Joseph J. G.

    1977-01-01

    Demonstrates how to find some canonical transformations without solving the Hamilton-Jacobi equation. Constructs the transformations from the harmonic oscillator to the free particle and uses these as examples of transformations that cannot be maintained when going from classical to quantum systems. (MLH)

  11. Infants' Recognition of Objects Using Canonical Color

    Science.gov (United States)

    Kimura, Atsushi; Wada, Yuji; Yang, Jiale; Otsuka, Yumiko; Dan, Ippeita; Masuda, Tomohiro; Kanazawa, So; Yamaguchi, Masami K.

    2010-01-01

    We explored infants' ability to recognize the canonical colors of daily objects, including two color-specific objects (human face and fruit) and a non-color-specific object (flower), by using a preferential looking technique. A total of 58 infants between 5 and 8 months of age were tested with a stimulus composed of two color pictures of an object…

  12. Kuidas Canon suureks kasvas / Andres Eilart

    Index Scriptorium Estoniae

    Eilart, Andres

    2004-01-01

    Jaapani kaamerate ja büroomasinate tootja Canon Groupi arengust, tegevusest kolmes regioonis - USA-s, Euroopas ja Aasias ning ettevõtte pikaajalise edu põhjustest - ärifilosoofiast ning ajastatud tootearendusest. Vt. samas: Firma esialgne nimi oli Kwanon; Konkurendid koonduvad

  13. Generalization of a few results in Integer Partitions

    CERN Document Server

    Dastidar, Manosij Ghosh

    2011-01-01

    In this paper, we generalize a few important results in Integer Partitions; namely the results known as Stanley's theorem and Elder's theorem, and the congruence results proposed by Ramanujan for the partition function. We generalize the results of Stanley and Elder from a fixed integer to an array of subsequent integers, and propose an analogue of Ramanujan's congruence relations for the `number of parts' function instead of the partition function. We also deduce the generating function for the `number of parts', and relate the technical results with their graphical interpretations through a novel use of the Ferrer's diagrams.

  14. Canonical brackets of a toy model for the Hodge theory without its canonical conjugate momenta

    CERN Document Server

    Shukla, D; Malik, R P

    2014-01-01

    We consider the toy model of a rigid rotor as an example of the Hodge theory within the framework of the Becchi-Rouet-Stora-Tyutin (BRST) formalism and show that the internal symmetries of this theory lead to the derivation of canonical brackets amongst the creation and annihilation operators of the dynamical variables where the definition of the canonical conjugate momenta is not required. We invoke only the spin-statistics theorem, normal ordering and basic concepts of continuous symmetries (and their generators) to derive the canonical brackets for the model of a one (0 + 1)-dimensional (1D) rigid rotor without using the definition of the canonical conjugate momenta anywhere. Our present method of derivation of the basic brackets is conjectured to be true for a class of theories that provide a set of tractable physical examples for the Hodge theory.

  15. Efficient computations of quantum canonical Gibbs state in phase space.

    Science.gov (United States)

    Bondar, Denys I; Campos, Andre G; Cabrera, Renan; Rabitz, Herschel A

    2016-06-01

    The Gibbs canonical state, as a maximum entropy density matrix, represents a quantum system in equilibrium with a thermostat. This state plays an essential role in thermodynamics and serves as the initial condition for nonequilibrium dynamical simulations. We solve a long standing problem for computing the Gibbs state Wigner function with nearly machine accuracy by solving the Bloch equation directly in the phase space. Furthermore, the algorithms are provided yielding high quality Wigner distributions for pure stationary states as well as for Thomas-Fermi and Bose-Einstein distributions. The developed numerical methods furnish a long-sought efficient computation framework for nonequilibrium quantum simulations directly in the Wigner representation. PMID:27415384

  16. Canonical transformation for trapped/passing guiding-center orbits in axisymmetric tokamak geometry

    Energy Technology Data Exchange (ETDEWEB)

    Brizard, Alain J. [Department of Physics, Saint Michael' s College, Colchester, Vermont 05439 (United States); Duthoit, François-Xavier [CEA, IRFM, F-13108 Saint-Paul-lez-Durance (France); SNU Division of Graduate Education for Sustainabilization of Foundation Energy, Seoul National University, Seoul 151-742 (Korea, Republic of)

    2014-05-15

    The generating function for the canonical transformation from the parallel canonical coordinates (s,p{sub ||}) to the action-angle coordinates (ζ, J) for trapped/passing guiding-center orbits in axisymmetric tokamak geometry is presented. Drawing on the analogy between the phase-space portraits of the librating/rotating pendulum and the trapped/passing guiding-center orbits, the generating function is expressed in terms of the Jacobi zeta function, which can then readily be used to obtain an explicit expression for the bounce-center transformation for trapped/passing-particle guiding-center orbits in axisymmetric tokamak geometry.

  17. Splitting K-symplectic methods for non-canonical separable Hamiltonian problems

    Science.gov (United States)

    Zhu, Beibei; Zhang, Ruili; Tang, Yifa; Tu, Xiongbiao; Zhao, Yue

    2016-10-01

    Non-canonical Hamiltonian systems have K-symplectic structures which are preserved by K-symplectic numerical integrators. There is no universal method to construct K-symplectic integrators for arbitrary non-canonical Hamiltonian systems. However, in many cases of interest, by using splitting, we can construct explicit K-symplectic methods for separable non-canonical systems. In this paper, we identify situations where splitting K-symplectic methods can be constructed. Comparative numerical experiments in three non-canonical Hamiltonian problems show that symmetric/non-symmetric splitting K-symplectic methods applied to the non-canonical systems are more efficient than the same-order Gauss' methods/non-symmetric symplectic methods applied to the corresponding canonicalized systems; for the non-canonical Lotka-Volterra model, the splitting algorithms behave better in efficiency and energy conservation than the K-symplectic method we construct via generating function technique. In our numerical experiments, the favorable energy conservation property of the splitting K-symplectic methods is apparent.

  18. Partitional clustering algorithms

    CERN Document Server

    2015-01-01

    This book summarizes the state-of-the-art in partitional clustering. Clustering, the unsupervised classification of patterns into groups, is one of the most important tasks in exploratory data analysis. Primary goals of clustering include gaining insight into, classifying, and compressing data. Clustering has a long and rich history that spans a variety of scientific disciplines including anthropology, biology, medicine, psychology, statistics, mathematics, engineering, and computer science. As a result, numerous clustering algorithms have been proposed since the early 1950s. Among these algorithms, partitional (nonhierarchical) ones have found many applications, especially in engineering and computer science. This book provides coverage of consensus clustering, constrained clustering, large scale and/or high dimensional clustering, cluster validity, cluster visualization, and applications of clustering. Examines clustering as it applies to large and/or high-dimensional data sets commonly encountered in reali...

  19. Supersymmetric Gauge Theories with Matters, Toric Geometries and Random Partitions

    CERN Document Server

    Noma, Y

    2006-01-01

    We derive the relation between the Hilbert space of certain geometries under the Bohr-Sommerfeld quantization and the perturbative prepotentials for the supersymmetric five-dimensional SU(N) gauge theories with massive fundamental matters and with one massive adjoint matter. The gauge theory with one adjoint matter shows interesting features. A five-dimensional generalization of Nekrasov's partition function can be written as a correlation function of two-dimensional chiral bosons and as a partition function of a statistical model of partitions. From a ground state of the statistical model we reproduce the polyhedron which characterizes the Hilbert space.

  20. An introduction to the theory of canonical matrices

    CERN Document Server

    Turnbull, H W

    2004-01-01

    Thorough and self-contained, this penetrating study of the theory of canonical matrices presents a detailed consideration of all the theory's principal features. Topics include elementary transformations and bilinear and quadratic forms; canonical reduction of equivalent matrices; subgroups of the group of equivalent transformations; and rational and classical canonical forms. The final chapters explore several methods of canonical reduction, including those of unitary and orthogonal transformations. 1952 edition. Index. Appendix. Historical notes. Bibliographies. 275 problems.

  1. Introduction to Modern Canonical Quantum General Relativity

    CERN Document Server

    Thiemann, T

    2001-01-01

    This is an introduction to the by now fifteen years old research field of canonical quantum general relativity, sometimes called "loop quantum gravity". The term "modern" in the title refers to the fact that the quantum theory is based on formulating classical general relativity as a theory of connections rather than metrics as compared to in original version due to Arnowitt, Deser and Misner. Canonical quantum general relativity is an attempt to define a mathematically rigorous, non-perturbative, background independent theory of Lorentzian quantum gravity in four spacetime dimensions in the continuum. The approach is minimal in that one simply analyzes the logical consequences of combining the principles of general relativity with the principles of quantum mechanics. The requirement to preserve background independence has lead to new, fascinating mathematical structures which one does not see in perturbative approaches, e.g. a fundamental discreteness of spacetime seems to be a prediction of the theory provi...

  2. Canonical approach to 2D induced gravity

    CERN Document Server

    Popovic, D

    2001-01-01

    Using canonical method the Liouville theory has been obtained as a gravitational Wess-Zumino action of the Polyakov string. From this approach it is clear that the form of the Liouville action is the consequence of the bosonic representation of the Virasoro algebra, and that the coefficient in front of the action is proportional to the central charge and measures the quantum braking of the classical symmetry.

  3. On Complex Supermanifolds with Trivial Canonical Bundle

    CERN Document Server

    Groeger, Josua

    2016-01-01

    We give an algebraic characterisation for the triviality of the canonical bundle of a complex supermanifold in terms of a certain Batalin-Vilkovisky superalgebra structure. As an application, we study the Calabi-Yau case, in which an explicit formula in terms of the Levi-Civita connection is achieved. Our methods include the use of complex integral forms and the recently developed theory of superholonomy.

  4. Quaternion Fourier and Linear Canonical Inversion Theorems

    OpenAIRE

    Hu, Xiao Xiao; Kou, Kit Ian

    2016-01-01

    The Quaternion Fourier transform (QFT) is one of the key tools in studying color image processing. Indeed, a deep understanding of the QFT has created the color images to be transformed as whole, rather than as color separated component. In addition, understanding the QFT paves the way for understanding other integral transform, such as the Quaternion Fractional Fourier transform (QFRFT), Quaternion linear canonical transform (QLCT) and Quaternion Wigner-Ville distribution. The aim of this pa...

  5. Canonical Energy is Quantum Fisher Information

    CERN Document Server

    Lashkari, Nima

    2015-01-01

    In quantum information theory, Fisher Information is a natural metric on the space of perturbations to a density matrix, defined by calculating the relative entropy with the unperturbed state at quadratic order in perturbations. In gravitational physics, Canonical Energy defines a natural metric on the space of perturbations to spacetimes with a Killing horizon. In this paper, we show that the Fisher information metric for perturbations to the vacuum density matrix of a ball-shaped region B in a holographic CFT is dual to the canonical energy metric for perturbations to a corresponding Rindler wedge R_B of Anti-de-Sitter space. Positivity of relative entropy at second order implies that the Fisher information metric is positive definite. Thus, for physical perturbations to anti-de-Sitter spacetime, the canonical energy associated to any Rindler wedge must be positive. This second-order constraint on the metric extends the first order result from relative entropy positivity that physical perturbations must sat...

  6. Interaction of n-octyl β,D-glucopyranoside with giant magnetic-fluid-loaded phosphatidylcholine vesicles: direct visualization of membrane curvature fluctuations as a function of surfactant partitioning between water and lipid bilayer.

    Science.gov (United States)

    Ménager, Christine; Guemghar, Dihya; Cabuil, Valérie; Lesieur, Sylviane

    2010-10-01

    The present study deals with the morphological modifications of giant dioleoyl phosphatidylcholine vesicles (DOPC GUVs) induced by the nonionic surfactant n-octyl β,D-glucopyranoside at sublytic levels, i.e., in the first steps of the vesicle-to-micelle transition process, when surfactant inserts into the vesicle bilayer without disruption. Experimental conditions were perfected to exactly control the surfactant bilayer composition of the vesicles, in line with former work focused on the mechanical properties of the membrane of magnetic-fluid-loaded DOPC GUVs submitted to a magnetic field. The purpose here was to systematically examine, in the absence of any external mechanical constraint, the dynamics of giant vesicle shape and membrane deformations as a function of surfactant partitioning between the aqueous phase and the lipid membrane, beforehand established by turbidity measurements from small unilamellar vesicles. PMID:20825201

  7. Crystal/liquid partitioning in augite - Effects of cooling rate

    Science.gov (United States)

    Gamble, R. P.; Taylor, L. A.

    1980-01-01

    The partitioning of major and minor elements between augite and melt was determined as a function of cooling rate for two high-titanium basalt compositions. The results of this study of lunar rock systems 10017 and 75055 were compared with the results of other kinetic studies of augite-liquid partitioning in other rock systems. It was found that the partitioning of major elements (i.e., Ca, Fe, Mg) is essentially rate independent and is insensitive to bulk rock composition and to the nature and order of appearance of coexisting phases for cooling rates of less than 100 C/hr. The partitioning behavior of minor elements (i.e., Al, Cr, Ti) for the same range of cooling rates is complex, being dependent on cooling rate and bulk rock composition. Consideration of these factors is important when augite chemistry and/or partitioning behavior are used in modeling certain magmatic processes or in estimating the thermal history of basaltic rocks.

  8. Development of partitioning method

    International Nuclear Information System (INIS)

    A partitioning method has been developed under the concepts of separating radioactive nuclides from a high-level waste according to their half lives and radioactive toxicity, and of disposing the waste safely. The partitioning test using about 18 liters (--220Ci) of the fuel reprocessing waste prepared at PNC has been started in October of 1982. In this test the behavior of radioactive nuclides was made clear. The present paper describes chemical behavior of non-radioactive elements contained in the high-level liquid waste in the extraction with di-isodecyl phosphoric acid (DIDPA). Distribution ratios of most of metal ions for DIDPA were less than 0.05, except that those of Mo, Zr and Fe were higher than 7. Ferric ion could not be back-extracted with 4 M HNO3, but with 0.5 M (COOH)2. In the extractiion with DIDPA, the third phase, which causes closing the settling banks or the flow paths in a mixer settler, was formed when the ferric ion concentration was over 0.02 M. This unfavorable phenomenon, however, was found to be suppressed by diluting the ferric ion concentration to lower than 0.01 M or by reducing ferric ion to ferrous ion. (author)

  9. Canonical Huffman code based full-text index

    Institute of Scientific and Technical Information of China (English)

    Yi Zhang; Zhili Pei; Jinhui Yang; Yanchun Liang

    2008-01-01

    Full-text indices are data structures that can be used to find any substring of a given string. Many full-text indices require space larger than the original string. In this paper, we introduce the canonical Huffman code to the wavelet tree of a string T[1...n]. Compared with Huffman code based wavelet tree, the memory space used to represent the shape of wavelet tree is not needed. In case of large alphabet, this part of memory is not negligible. The operations of wavelet tree are also simpler and more efficient due to the canonical Huffman code. Based on the resulting structure, the multi-key rank and select functions can be performed using at most nH0 + |X|(lglgn + lgn - lg|Σ|)+O(nH0) bits and in O(H0) time for average cases, where H0 is the zeroth order empirical entropy of T. In the end, we present an efficient construction algorithm for this index, which is on-line and linear.

  10. Canonical group quantization and boundary conditions

    Energy Technology Data Exchange (ETDEWEB)

    Jung, Florian

    2012-07-16

    In the present thesis, we study quantization of classical systems with non-trivial phase spaces using the group-theoretical quantization technique proposed by Isham. Our main goal is a better understanding of global and topological aspects of quantum theory. In practice, the group-theoretical approach enables direct quantization of systems subject to constraints and boundary conditions in a natural and physically transparent manner -- cases for which the canonical quantization method of Dirac fails. First, we provide a clarification of the quantization formalism. In contrast to prior treatments, we introduce a sharp distinction between the two group structures that are involved and explain their physical meaning. The benefit is a consistent and conceptually much clearer construction of the Canonical Group. In particular, we shed light upon the 'pathological' case for which the Canonical Group must be defined via a central Lie algebra extension and emphasise the role of the central extension in general. In addition, we study direct quantization of a particle restricted to a half-line with 'hard wall' boundary condition. Despite the apparent simplicity of this example, we show that a naive quantization attempt based on the cotangent bundle over the half-line as classical phase space leads to an incomplete quantum theory; the reflection which is a characteristic aspect of the 'hard wall' is not reproduced. Instead, we propose a different phase space that realises the necessary boundary condition as a topological feature and demonstrate that quantization yields a suitable quantum theory for the half-line model. The insights gained in the present special case improve our understanding of the relation between classical and quantum theory and illustrate how contact interactions may be incorporated.

  11. Canonical group quantization and boundary conditions

    International Nuclear Information System (INIS)

    In the present thesis, we study quantization of classical systems with non-trivial phase spaces using the group-theoretical quantization technique proposed by Isham. Our main goal is a better understanding of global and topological aspects of quantum theory. In practice, the group-theoretical approach enables direct quantization of systems subject to constraints and boundary conditions in a natural and physically transparent manner -- cases for which the canonical quantization method of Dirac fails. First, we provide a clarification of the quantization formalism. In contrast to prior treatments, we introduce a sharp distinction between the two group structures that are involved and explain their physical meaning. The benefit is a consistent and conceptually much clearer construction of the Canonical Group. In particular, we shed light upon the 'pathological' case for which the Canonical Group must be defined via a central Lie algebra extension and emphasise the role of the central extension in general. In addition, we study direct quantization of a particle restricted to a half-line with 'hard wall' boundary condition. Despite the apparent simplicity of this example, we show that a naive quantization attempt based on the cotangent bundle over the half-line as classical phase space leads to an incomplete quantum theory; the reflection which is a characteristic aspect of the 'hard wall' is not reproduced. Instead, we propose a different phase space that realises the necessary boundary condition as a topological feature and demonstrate that quantization yields a suitable quantum theory for the half-line model. The insights gained in the present special case improve our understanding of the relation between classical and quantum theory and illustrate how contact interactions may be incorporated.

  12. Theory of extreme correlations using canonical Fermions and path integrals

    Energy Technology Data Exchange (ETDEWEB)

    Shastry, B. Sriram, E-mail: sriram@physics.ucsc.edu

    2014-04-15

    The  t–J  model is studied using a novel and rigorous mapping of the Gutzwiller projected electrons, in terms of canonical electrons. The mapping has considerable similarity to the Dyson–Maleev transformation relating spin operators to canonical Bosons. This representation gives rise to a non Hermitian quantum theory, characterized by minimal redundancies. A path integral representation of the canonical theory is given. Using it, the salient results of the extremely correlated Fermi liquid (ECFL) theory, including the previously found Schwinger equations of motion, are easily rederived. Further, a transparent physical interpretation of the previously introduced auxiliary Greens function and the ‘caparison factor’, is obtained. The low energy electron spectral function in this theory, with a strong intrinsic asymmetry, is summarized in terms of a few expansion coefficients. These include an important emergent energy scale Δ{sub 0} that shrinks to zero on approaching the insulating state, thereby making it difficult to access the underlying very low energy Fermi liquid behavior. The scaled low frequency ECFL spectral function, related simply to the Fano line shape, has a peculiar energy dependence unlike that of a Lorentzian. The resulting energy dispersion obtained by maximization is a hybrid of a massive and a massless Dirac spectrum E{sub Q}{sup ∗}∼γQ−√(Γ{sub 0}{sup 2}+Q{sup 2}), where the vanishing of Q, a momentum type variable, locates the kink minimum. Therefore the quasiparticle velocity interpolates between (γ∓1) over a width Γ{sub 0} on the two sides of Q=0, implying a kink there that strongly resembles a prominent low energy feature seen in angle resolved photoemission spectra (ARPES) of cuprate materials. We also propose novel ways of analyzing the ARPES data to isolate the predicted asymmetry between particle and hole excitations. -- Highlights: •Spectral function of the Extremely Correlated Fermi Liquid theory at low energy.

  13. Kato expansion in quantum canonical perturbation theory

    Science.gov (United States)

    Nikolaev, Andrey

    2016-06-01

    This work establishes a connection between canonical perturbation series in quantum mechanics and a Kato expansion for the resolvent of the Liouville superoperator. Our approach leads to an explicit expression for a generator of a block-diagonalizing Dyson's ordered exponential in arbitrary perturbation order. Unitary intertwining of perturbed and unperturbed averaging superprojectors allows for a description of ambiguities in the generator and block-diagonalized Hamiltonian. We compare the efficiency of the corresponding computational algorithm with the efficiencies of the Van Vleck and Magnus methods for high perturbative orders.

  14. HPAM: Hirshfeld partitioned atomic multipoles

    Science.gov (United States)

    Elking, Dennis M.; Perera, Lalith; Pedersen, Lee G.

    2012-02-01

    molecular charge density ρ(r) is partitioned into Hirshfeld (HD) and Hirshfeld-Iterated (HD-I) atomic charge densities ρ(r) on a grid. Atomic charges q and multipoles Qlma are calculated from the partitioned atomic charge densities ρ(r) by numerical integration. Solution method: Molecular and isolated atomic grids are generated for the molecule of interest. The ab initio density matrix P and basis functions χ(r) are read in from 'formatted checkpoint' files obtained from the Gaussian 03 or 09 quantum chemistry programs. The ab initio density is evaluated for the molecule and the isolated atoms/atomic ions on grids and used to construct Hirshfeld (HD) and Hirshfeld-I (HD-I) partitioned atomic charges densities ρ(r), which are used to calculate atomic charges q and atomic multipoles Qlma by integration. Restrictions: The ab initio density matrix can be calculated at the HF, DFT, MP2, or CCSD levels with ab initio Gaussian basis sets that include up to s, p, d, f, g functions for either closed shell or open shell molecules. Running time: The running time varies with the size of the molecule, the size of the ab initio basis set, and the coarseness of the desired grid. The run time can range from a minute or less for water to ˜15 minutes for neopentane.

  15. Avicenna's Canon of Medicine: a look at health, public health, and environmental sanitation.

    Science.gov (United States)

    Saffari, Mohsen; Pakpour, Amir H

    2012-12-01

    Avicenna, a renowned Persian Muslim scientist has written numerous scientific papers and valuable medical books that are respected worldwide. For centuries his masterpiece, the "Canon of Medicine", has been used as a major medical reference. The Canon, as a prime encyclopedia on medicine is comprised of five books. In the introduction to the Canon, Avicenna has described the purpose of medicine as the preservation of health if it is already attained and its restoration when it is lost. He defines health as a trait or state, which results in the normal functioning of the human body and presumes that health is a steady state, whilst disease is more of a variable concept. Thus whenever we depart from a healthy state, we approach disease. A comparison of current views regarding definitions of health, disease and their components as defined by Avicenna could open new horizons for ancient, traditional medicine. The Canon contains numerous implications concerning the infrastructures of public health-related issues. For example the specifications of healthy water and air are well described in the "Canon of Medicine". To enable a better understanding of Avicenna's viewpoints about public health, we have briefly reviewed his perspective on the topics of health, disease, and environmental sanitation concerning water and air. PMID:23199255

  16. The grand partition function Z ({alpha},{beta}) of a quantum system is studied, using diagrammatic representations of the perturbation expansion; La grande fonction de partition Z ({alpha},{beta}) d'un systeme quantique est etudies en utilisant des representations diagrammatiques du developpement en serie des perturbations

    Energy Technology Data Exchange (ETDEWEB)

    Dominicis, C. de [Commissariat a l' Energie Atomique, Saclay (France).Centre d' Etudes Nucleaires

    1961-07-01

    The grand partition function Z ({alpha},{beta}) of a quantum system is studied, using diagrammatic representations of the perturbation expansion. For a fermions system, it is possible to show, by proper resummation, without approximations but under some 'regularity hypothesis', that Log Z ({alpha},{beta}) takes a form where, besides trivial dependences, {alpha} and {beta} only appear through a statistical factor F{sub k}{sup -} = [1 + e{sup -{alpha}}{sup +{beta}}{sup {epsilon}{sub k}{sup 0}}{sup -{beta}}{sup W{sub k}}]{sup -1}. W{sub k} is a (real) self-consistent potential, generalized to all orders and can be defined by a stationary condition on Log Z ({alpha},{beta}) under variations of F{sub k}{sup -}. The thermodynamical quantities take a form analogous to the expressions Landau introduced for the Fermi liquids. The zero temperature limit (for isotropic systems) gives back Goldstone expressions for the ground state of a system. (author) [French] La grande fonction de partition Z ({alpha},{beta}) d'un systeme quantique est etudiee en utilisant des representations diagrammatiques du developpement en serie des perturbations. Pour un systeme de fermions on peut, par des resommations adequates, sans approximations mais sous reserve d'une 'hypothese de regularite', mettre Log Z ({alpha},{beta}) sous une forme ou, en dehors de dependances triviales, {alpha} et {beta} n'interviennent que par l'intermediaire d'un facteur statistique F{sub k}{sup -} = [1 + e{sup -{alpha}}{sup +{beta}}{sup {epsilon}{sub k}{sup 0}}{sup -{beta}}{sup W{sub k}}]{sup -1}. W{sub k} est ici un potentiel self-consistant (reel) generalise a tous les ordres et peut etre defini par une condition de stationnarite de Log Z ({alpha},{beta}) pour des variations de F{sub k}{sup -}. Les grandeurs thermodynamiques prennent une forme analogue aux expressions que LANDAU a introduites pour les liquides de FERMI. A la limite de la temperature nulle (et pour un

  17. Canonical Transformations can Dramatically Simplify Supersymmetry

    CERN Document Server

    Dixon, John

    2016-01-01

    A useful way to keep track of the SUSY invariance of a theory is by formulating it with a BRST Poisson Bracket. It turns out that there is a crucial subtlety that is hidden in this formulation. When the theory contains a Chiral Multiplet, the relevant BRST Poisson Bracket has a very important Canonical Transformation that leaves it invariant. This Canonical Transformation takes all or part of the Scalar Field $A$ and replaces it with a Zinn Source $J_A$, and also takes the related Zinn Source $\\Gamma_A$ and replaces it with an `Antighost' Field $\\eta_A$. Naively, this looks like it is just a change of notation. But in fact the interpretation means that one has moved some of the conserved Noether SUSY current from the Field Action, and placed it partly in the Zinn Sources Action, and so the SUSY current in the Field part of the Action is no longer conserved, because the Zinn Sources do not satisfy any equations of motion. They are not quantized, because they are Sources. So it needs to be recognized that SUSY ...

  18. Face hallucination using orthogonal canonical correlation analysis

    Science.gov (United States)

    Zhou, Huiling; Lam, Kin-Man

    2016-05-01

    A two-step face-hallucination framework is proposed to reconstruct a high-resolution (HR) version of a face from an input low-resolution (LR) face, based on learning from LR-HR example face pairs using orthogonal canonical correlation analysis (orthogonal CCA) and linear mapping. In the proposed algorithm, face images are first represented using principal component analysis (PCA). Canonical correlation analysis (CCA) with the orthogonality property is then employed, to maximize the correlation between the PCA coefficients of the LR and the HR face pairs to improve the hallucination performance. The original CCA does not own the orthogonality property, which is crucial for information reconstruction. We propose using orthogonal CCA, which is proven by experiments to achieve a better performance in terms of global face reconstruction. In addition, in the residual-compensation process, a linear-mapping method is proposed to include both the inter- and intrainformation about manifolds of different resolutions. Compared with other state-of-the-art approaches, the proposed framework can achieve a comparable, or even better, performance in terms of global face reconstruction and the visual quality of face hallucination. Experiments on images with various parameter settings and blurring distortions show that the proposed approach is robust and has great potential for real-world applications.

  19. New constraints for canonical general relativity

    CERN Document Server

    Reisenberger, M

    1995-01-01

    Ashtekar's canonical theory of classical complex Euclidean GR (no Lorentzian reality conditions) is found to be invariant under the full algebra of infinitesimal 4-diffeomorphisms, but non-invariant under some finite proper 4-diffeos when the densitized dreibein, \\tilE^a_i, is degenerate. The breakdown of 4-diffeo invariance appears to be due to the inability of the Ashtekar Hamiltonian to generate births and deaths of \\tilE flux loops (leaving open the possibility that a new `causality condition' forbidding the birth of flux loops might justify the non-invariance of the theory). A fully 4-diffeo invariant canonical theory in Ashtekar's variables, derived from Plebanski's action, is found to have constraints that are stronger than Ashtekar's for rank\\tilE < 2. The corresponding Hamiltonian generates births and deaths of \\tilE flux loops. It is argued that this implies a finite amplitude for births and deaths of loops in the physical states of quantum GR in the loop representation, thus modifying this (part...

  20. Canonical-basis time-dependent Hartree-Fock-Bogoliubov theory and linear-response calculations

    CERN Document Server

    Ebata, Shuichiro; Inakura, Tsunenori; Yoshida, Kenichi; Hashimoto, Yukio; Yabana, Kazuhiro

    2010-01-01

    We present simple equations for a canonical-basis formulation of the time-dependent Hartree-Fock-Bogoliubov (TDHFB) theory. The equations are obtained from the TDHFB theory with an approximation that the pair potential is assumed to be diagonal in the canonical basis. The canonical-basis formulation significantly reduces the computational cost. We apply the method to linear-response calculations for even-even light nuclei and demonstrate its capability and accuracy by comparing our results with recent calculations of the quasi-particle random-phase approximation with Skyrme functionals. We show systematic studies of E1 strength distributions for Ne and Mg isotopes. The evolution of the low-lying pygmy strength seems to be determined by the interplay of several factors, including the neutron excess, separation energy, neutron shell effects, deformation, and pairing.

  1. Canon Fodder: Young Adult Literature as a Tool for Critiquing Canonicity

    Science.gov (United States)

    Hateley, Erica

    2013-01-01

    Young adult literature is a tool of socialisation and acculturation for young readers. This extends to endowing "reading" with particular significance in terms of what literature should be read and why. This paper considers some recent young adult fiction with an eye to its engagement with canonical literature and its representations of…

  2. An obstruction to the existence of anti-canonically balanced metrics on Fano manifolds

    OpenAIRE

    Saito, Shunsuke; Takahashi, Ryosuke

    2016-01-01

    We introduce a new obstruction to the existence of anti-canonically balanced metrics by studying the asymptotic behavior of the quantized Ding functional along Bergman geodesic rays associated to special test configurations. We also discuss some relation between our new stability and asymptotic Chow stability.

  3. Definition of a time variable with entropy of a perfect fluid in canonical quantum gravity

    International Nuclear Information System (INIS)

    The Brown-Kuchar mechanism is applied in the case of general relativity coupled with Schutz' model for a perfect fluid. Using the canonical formalism and manipulating the set of modified constraints one is able to recover the definition of a time-evolution operator, i.e. a physical Hamiltonian, expressed as a functional of gravitational variables and the entropy.

  4. Definition of a time variable with Entropy of a perfect fluid in Canonical Quantum Gravity

    OpenAIRE

    Cianfrani, Francesco; Montani, Giovanni; Zonetti, Simone

    2008-01-01

    The Brown-Kuchar mechanism is applied in the case of General Relativity coupled with the Schutz model for a perfect fluid. Using the canonical formalism and manipulating the set of modified constraints one is able to recover the definition of a time evolution operator, i.e. a physical Hamiltonian, expressed as a functional of gravitational variables and the entropy.

  5. Point Canonical Transformation for Solving Five-Parameter Exponential-Type Potential

    Institute of Scientific and Technical Information of China (English)

    YANG Jin; XIANG An-Ping; YU Wan-Lun

    2003-01-01

    Using the approach of mapping of shape invariant potentials under point canonical transformations, the energy spectra and wave functions are most easily determined for the bound states of the five-parameter exponential-type potential with a little extra effort.

  6. India and Pakistan: Partition Lessons

    DEFF Research Database (Denmark)

    Kaur, Ravinder

    2007-01-01

    The violent territorial rupture of 1947 and its legacy reveal partition to be conceptually flawed and historically ill-grounded as a solution to political antagonism, says Ravinder Kaur.......The violent territorial rupture of 1947 and its legacy reveal partition to be conceptually flawed and historically ill-grounded as a solution to political antagonism, says Ravinder Kaur....

  7. [Huang Yizhou's study on Nei jing (Inner Canon)].

    Science.gov (United States)

    Hu, Benxiang; Huang, Youmei; Yu, Chengfen

    2002-01-01

    Being a great classical scholar of the late Qing dynasty, Huang Yizhou collated Nei jing (Inner Canon) by textual criticism. But most of his works were missing. By reviewing historical documents and literature, it has been found that his collated books include Huang di nei jing su wen jiao ben (Collated Edition of Huangdi's Inner Canon Plain Questions), Huang di nei jing su wen chong jiao zheng (Recollated Huangdi's Inner Canon Plain Questions), Nei jing zhen ci (Acupuncture in Inner Canon), Huang di nei jing jiu juan ji zhu (Variorum of Nine Volumes of Huangdi's Inner Canon), Huang di nei jing ming tang (Acupuncture Chart of Huangdi's Inner Canon), and Jiu chao tai su jiao ben (Old Extremely Plain Question Recension). Many of his disciples became famous scholars in the Republican period. PMID:12015056

  8. Integral Canonical Models for Automorphic Vector Bundles of Abelian Type

    OpenAIRE

    Lovering, Tom

    2016-01-01

    We define and construct integral canonical models for automorphic vector bundles over Shimura varieties of abelian type. More precisely, we first build on Kisin's work to construct integral canonical models over rings of integers of number fields with finitely many primes inverted for Shimura varieties of abelian type with hyperspecial level at all primes we do not invert, compatible with Kisin's construction. We then define a notion of an integral canonical model for the standard principal b...

  9. Canonical symmetry properties of the constrained singular generalized mechanical system

    Institute of Scientific and Technical Information of China (English)

    李爱民; 江金环; 李子平

    2003-01-01

    Based on generalized Apell-Chetaev constraint conditions and to take the inherent constrains for singular Lagrangian into account, the generalized canonical equations for a general mechanical system with a singular higher-order Lagrangian and subsidiary constrains are formulated. The canonical symmetries in phase space for such a system are studied and Noether theorem and its inversion theorem in the generalized canonical formalism have been established.

  10. Canonical symmetry properties of the constrained singular generalized mechanical system

    Institute of Scientific and Technical Information of China (English)

    LiAi-Min; JiangJin-Huan; LiZi-Ping

    2003-01-01

    Based on generalized Apell-Chetaev constraint conditions and to take the inherent constrains for singular Lagrangian into account,the generalized canonical equations for a general mechanical system with a singular higher-order Lagrangian and subsidiary constrains are formulated. The canonical symmetries in phase space for such a system are studied and Noether theorem and its inversion theorem in the generalized canonical formalism have been established.

  11. A NOVEL ALGORITHM FOR VOICE CONVERSION USING CANONICAL CORRELATION ANALYSIS

    Institute of Scientific and Technical Information of China (English)

    Jian Zhihua; Yang Zhen

    2008-01-01

    A novel algorithm for voice conversion is proposed in this paper. The mapping function of spectral vectors of the source and target speakers is calculated by the Canonical Correlation Analysis(CCA) estimation based on Gaussian mixture models. Since the spectral envelope feature remains a majority of second order statistical information contained in speech after Linear Prediction Coding(LPC) analysis, the CCA method is more suitable for spectral conversion than Minimum Mean Square Error (MMSE) because CCA explicitly considers the variance of each component of the spectral vectors during conversion procedure. Both objective evaluations and subjective listening tests are conducted. The experimental results demonstrate that the proposed scheme can achieve better performance than the previous method which uses MMSE estimation criterion.

  12. The Geometry of Tangent Bundles: Canonical Vector Fields

    Directory of Open Access Journals (Sweden)

    Tongzhu Li

    2013-01-01

    Full Text Available A canonical vector field on the tangent bundle is a vector field defined by an invariant coordinate construction. In this paper, a complete classification of canonical vector fields on tangent bundles, depending on vector fields defined on their bases, is obtained. It is shown that every canonical vector field is a linear combination with constant coefficients of three vector fields: the variational vector field (canonical lift, the Liouville vector field, and the vertical lift of a vector field on the base of the tangent bundle.

  13. Intersubject information mapping: revealing canonical representations of complex natural stimuli

    Directory of Open Access Journals (Sweden)

    Nikolaus Kriegeskorte

    2015-03-01

    Full Text Available Real-world time-continuous stimuli such as video promise greater naturalism for studies of brain function. However, modeling the stimulus variation is challenging and introduces a bias in favor of particular descriptive dimensions. Alternatively, we can look for brain regions whose signal is correlated between subjects, essentially using one subject to model another. Intersubject correlation mapping (ICM allows us to find brain regions driven in a canonical manner across subjects by a complex natural stimulus. However, it requires a direct voxel-to-voxel match between the spatiotemporal activity patterns and is thus only sensitive to common activations sufficiently extended to match up in Talairach space (or in an alternative, e.g. cortical-surface-based, common brain space. Here we introduce the more general approach of intersubject information mapping (IIM. For each brain region, IIM determines how much information is shared between the subjects' local spatiotemporal activity patterns. We estimate the intersubject mutual information using canonical correlation analysis applied to voxels within a spherical searchlight centered on each voxel in turn. The intersubject information estimate is invariant to linear transforms including spatial rearrangement of the voxels within the searchlight. This invariance to local encoding will be crucial in exploring fine-grained brain representations, which cannot be matched up in a common space and, more fundamentally, might be unique to each individual – like fingerprints. IIM yields a continuous brain map, which reflects intersubject information in fine-grained patterns. Performed on data from functional magnetic resonance imaging (fMRI of subjects viewing the same television show, IIM and ICM both highlighted sensory representations, including primary visual and auditory cortices. However, IIM revealed additional regions in higher association cortices, namely temporal pole and orbitofrontal cortex. These

  14. Consistency of canonical formulation of Horava gravity

    Energy Technology Data Exchange (ETDEWEB)

    Soo, Chopin, E-mail: cpsoo@mail.ncku.edu.tw [Department of Physics, National Cheng Kung University, Tainan, Taiwan (China)

    2011-09-22

    Both the non-projectable and projectable version of Horava gravity face serious challenges. In the non-projectable version, the constraint algebra is seemingly inconsistent. The projectable version lacks a local Hamiltonian constraint, thus allowing for an extra graviton mode which can be problematic. A new formulation (based on arXiv:1007.1563) of Horava gravity which is naturally realized as a representation of the master constraint algebra (instead of the Dirac algebra) studied by loop quantum gravity researchers is presented. This formulation yields a consistent canonical theory with first class constraints; and captures the essence of Horava gravity in retaining only spatial diffeomorphisms as the physically relevant non-trivial gauge symmetry. At the same time the local Hamiltonian constraint is equivalently enforced by the master constraint.

  15. Comments on the Canonical Measure in Cosmology

    CERN Document Server

    Kaya, Ali

    2012-01-01

    In the mini-superspace approximation to cosmology, the canonical measure can be used to compute probabilities when a cutoff is introduced in the phase space to regularize the divergent measure. However, the region initially constrained by a simple cutoff evolves non-trivially under the Hamiltonian flow. We determine the deformation of the regularized phase space along the orbits when a cutoff is introduced for the scale factor of the universe or for the Hubble parameter. In the former case, we find that the cutoff for the scale factor varies in the phase space and effectively decreases as one evolves backwards in time. In the later case, we calculate the probability of slow-roll inflation in a chaotic model with a massive scalar, which turns out to be cutoff dependent but not exponentially suppressed. We also investigate the measure problem for non-abelian gauge fields giving rise to inflation.

  16. The Deuteron as a Canonically Quantized Biskyrmion

    CERN Document Server

    Acus, A; Norvaisas, E; Riska, D O

    2003-01-01

    The ground state configurations of the solution to Skyrme's topological soliton model for systems with baryon number larger than 1 are well approximated with rational map ans"atze, without individual baryon coordinates. Here canonical quantization of the baryon number 2 system, which represents the deuteron, is carried out in the rational map approximation. The solution, which is described by the 6 parameters of the chiral group SU(2)$times$SU(2), is stabilized by the quantum corrections. The matter density of the variational quantized solution has the required exponential large distance falloff and the quantum numbers of the deuteron. Similarly to the axially symmetric semiclassical solution, the radius and the quadrupole moment are, however, only about half as large as the corresponding empirical values. The quantized deuteron solution is constructed for representations of arbitrary dimension of the chiral group.

  17. Linear canonical transforms theory and applications

    CERN Document Server

    Kutay, M; Ozaktas, Haldun; Sheridan, John

    2016-01-01

    This book provides a clear and accessible introduction to the essential mathematical foundations of linear canonical transforms from a signals and systems perspective. Substantial attention is devoted to how these transforms relate to optical systems and wave propagation. There is extensive coverage of sampling theory and fast algorithms for numerically approximating the family of transforms. Chapters on topics ranging from digital holography to speckle metrology provide a window on the wide range of applications. This volume will serve as a reference for researchers in the fields of image and signal processing, wave propagation, optical information processing and holography, optical system design and modeling, and quantum optics. It will be of use to graduate students in physics and engineering, as well as for scientists in other areas seeking to learn more about this important yet relatively unfamiliar class of integral transformations.

  18. Present status of partitioning developments

    International Nuclear Information System (INIS)

    Evolution and development of the concept of partitioning of high-level liquid wastes (HLLW) in nuclear fuel reprocessing are reviewed historically from the early phase of separating useful radioisotopes from HLLW to the recent phase of eliminating hazardous nuclides such as transuranium elements for safe waste disposal. Since the criteria in determining the nuclides for elimination and the respective decontamination factors are important in the strategy of partitioning, current views on the criteria are summarized. As elimination of the transuranium is most significant in the partitioning, various methods available of separating them from fission products are evaluated. (auth.)

  19. Square Partitions and Catalan Numbers

    OpenAIRE

    Bennett, Matthew; Chari, Vyjayanthi; Dolbin, R. J.; Manning, Nathan

    2009-01-01

    For each integer $k\\ge 1$, we define an algorithm which associates to a partition whose maximal value is at most $k$ a certain subset of all partitions. In the case when we begin with a partition $\\lambda$ which is square, i.e $\\lambda=\\lambda_1\\ge...\\ge\\lambda_k>0$, and $\\lambda_1=k,\\lambda_k=1$, then applying the algorithm $\\ell$ times gives rise to a set whose cardinality is either the Catalan number $c_{\\ell-k+1}$ (the self dual case) or twice the Catalan number. The algorithm defines a t...

  20. Partitioning ecosystems for sustainability.

    Science.gov (United States)

    Murray, Martyn G

    2016-03-01

    Decline in the abundance of renewable natural resources (RNRs) coupled with increasing demands of an expanding human population will greatly intensify competition for Earth's natural resources during this century, yet curiously, analytical approaches to the management of productive ecosystems (ecological theory of wildlife harvesting, tragedy of the commons, green economics, and bioeconomics) give only peripheral attention to the driving influence of competition on resource exploitation. Here, I apply resource competition theory (RCT) to the exploitation of RNRs and derive four general policies in support of their sustainable and equitable use: (1) regulate resource extraction technology to avoid damage to the resource base; (2) increase efficiency of resource use and reduce waste at every step in the resource supply chain and distribution network; (3) partition ecosystems with the harvesting niche as the basic organizing principle for sustainable management of natural resources by multiple users; and (4) increase negative feedback between consumer and resource to bring about long-term sustainable use. A simple policy framework demonstrates how RCT integrates with other elements of sustainability science to better manage productive ecosystems. Several problem areas of RNR management are discussed in the light of RCT, including tragedy of the commons, overharvesting, resource collapse, bycatch, single species quotas, and simplification of ecosystems.

  1. Incentives for partitioning, revisited

    International Nuclear Information System (INIS)

    The incentives for separating and eliminating various elements from radioactive waste prior to final geologic disposal were investigated. Exposure pathways to humans were defined, and potential radiation doses to an individual living within the region of influence of the underground storage site were calculated. The assumed radionuclide source was 1/5 of the accumulated high-level waste from the US nuclear power economy through the year 2000. The repository containing the waste was assumed to be located in a reference salt site geology. The study required numerous assumptions concerning the transport of radioactivity from the geologic storage site to man. The assumptions used maximized the estimated potential radiation doses, particularly in the case of the intrusion water well scenario, where hydrologic flow field dispersion effects were ignored. Thus, incentives for removing elements from the waste tended to be maximized. Incentives were also maximized by assuming that elements removed from the waste could be eliminated from the earth without risk. The results of the study indicate that for reasonable disposal conditions, incentives for partitioning any elements from the waste in order to minimize the risk to humans are marginal at best

  2. Partitioning ecosystems for sustainability.

    Science.gov (United States)

    Murray, Martyn G

    2016-03-01

    Decline in the abundance of renewable natural resources (RNRs) coupled with increasing demands of an expanding human population will greatly intensify competition for Earth's natural resources during this century, yet curiously, analytical approaches to the management of productive ecosystems (ecological theory of wildlife harvesting, tragedy of the commons, green economics, and bioeconomics) give only peripheral attention to the driving influence of competition on resource exploitation. Here, I apply resource competition theory (RCT) to the exploitation of RNRs and derive four general policies in support of their sustainable and equitable use: (1) regulate resource extraction technology to avoid damage to the resource base; (2) increase efficiency of resource use and reduce waste at every step in the resource supply chain and distribution network; (3) partition ecosystems with the harvesting niche as the basic organizing principle for sustainable management of natural resources by multiple users; and (4) increase negative feedback between consumer and resource to bring about long-term sustainable use. A simple policy framework demonstrates how RCT integrates with other elements of sustainability science to better manage productive ecosystems. Several problem areas of RNR management are discussed in the light of RCT, including tragedy of the commons, overharvesting, resource collapse, bycatch, single species quotas, and simplification of ecosystems. PMID:27209800

  3. 氨氮浓度对CANON工艺功能微生物丰度和群落结构的影响%Assessment of the Effect of Influent NH4+-N Concentration on the Abundance and Community Structure of Functional Bacteria in CANON Process

    Institute of Scientific and Technical Information of China (English)

    刘涛; 李冬; 曾辉平; 畅晓燕; 张杰

    2013-01-01

    为了研究CANON工艺在常温低氨氮基质条件下的宏观运行效能及微观生态系统,通过调节曝气量和水力停留时间(HRT)实现了CANON 工艺在不同进水氨氮浓度下的稳定运行,并基于PCR-DGGE和荧光定量PCR方法,分析了氨氮浓度对反应器中氨氧化细菌(AOB)和厌氧氨氧化菌(ANAMMOX菌)群落结构及丰度的影响.结果表明,较高氨氮环境中总氮去除负荷在1.0 g·(L·d)-1以上,当氨氮浓度降至100 mg·L-1时,总氮去除负荷明显降低.进水氨氮浓度对AOB的群落结构有重要影响,而对ANAMMOX菌群落影响较小.AOB和ANAMMOX菌的丰度随氨氮浓度的降低而减少,而亚硝酸盐氧化菌(NOB)的丰度随氨氮浓度的降低而增加,这可能是导致系统脱氮效果下降的主要原因.因此,需要通过一定的调控手段,减少AOB和ANAMMOX菌的损失,抑制NOB的生长,以便维持系统在低氨氮条件下的脱氮性能.%To investigate macroscopic performance and mierocosmic ecosystem of CANON process in low ammonium concentration at room temprature, a steady-operation CANON reactor was achieved in different ammonium concentrations by adjusting aeration and hydraulic retention time (HRT) , and the effect of ammonium concentration on the abundance and community structure of functional bacteria was analyzed using PCR-DGGE and real-time PCR. The results indicated a high TN removal loading of over 1.0 g·(L·d) -1 in relatively high ammonium which was significantly reduced with the ammonium concentration of 100 mg·L-1 . The community structure, of ammonium oxidizing bacteria ( AOB) changed sharply with the decrease of ammonium concentraion, which was not the same as anaerobic ammonium oxidizing bacteria ( ANAMMOX bacteria). Besides, the abundance of the two functional groups of bacteria reduced while the population of nitrite oxidizing bacteria ( NOB) rose with the decrease of ammonium, which might be the main reason for the reduction of nitrogen removal

  4. Transcriptional oscillation of canonical clock genes in mouse peripheral tissues

    Directory of Open Access Journals (Sweden)

    Nakahata Yasukazu

    2004-10-01

    Full Text Available Abstract Background The circadian rhythm of about 24 hours is a fundamental physiological function observed in almost all organisms from prokaryotes to humans. Identification of clock genes has allowed us to study the molecular bases for circadian behaviors and temporal physiological processes such as hormonal secretion, and has prompted the idea that molecular clocks reside not only in a central pacemaker, the suprachiasmatic nuclei (SCN of hypothalamus in mammals, but also in peripheral tissues, even in immortalized cells. Furthermore, previous molecular dissection revealed that the mechanism of circadian oscillation at a molecular level is based on transcriptional regulation of clock and clock-controlled genes. Results We systematically analyzed the mRNA expression of clock and clock-controlled genes in mouse peripheral tissues. Eight genes (mBmal1, mNpas2, mRev-erbα, mDbp, mRev-erbβ, mPer3, mPer1 and mPer2; given in the temporal order of the rhythm peak showed robust circadian expressions of mRNAs in all tissues except testis, suggesting that these genes are core molecules of the molecular biological clock. The bioinformatics analysis revealed that these genes have one or a combination of 3 transcriptional elements (RORE, DBPE, and E-box, which are conserved among human, mouse, and rat genome sequences, and indicated that these 3 elements may be responsible for the biological timing of expression of canonical clock genes. Conclusions The observation of oscillatory profiles of canonical clock genes is not only useful for physiological and pathological examination of the circadian clock in various organs but also important for systematic understanding of transcriptional regulation on a genome-wide basis. Our finding of the oscillatory expression of canonical clock genes with a temporal order provides us an interesting hypothesis, that cyclic timing of all clock and clock-controlled genes may be dependent on several transcriptional elements

  5. The "cause of Jesus" (Sache Jesu as the Canon behind the Canon

    Directory of Open Access Journals (Sweden)

    Andries G. van Aarde

    2001-01-01

    Full Text Available God, and not the Bible as such, is the church's primary authority. Jesus of Nazareth is the manifestation of God in history. In a post-Aufkllirung environment one cannot escape the demand to think historically. To discern what could be seen as the "ground" offaith, one needs to distinguish the "proclaiming Jesus" from the "proclaimed Jesus", though these two aspects are dialectically intertwined. This dialeclic can be described as the "Jesus kerygma" or the "cause of Jesus". The aim of this article is to argue that if Christians focus only on the church's kerygma they base their ultimate trust upon assertions of faith, rather than upon the cause of faith. The dictum that the cause of Jesus is the canon behind the canon is explained in terms of the distinction between ''fides qua creditur" and "fides quae creditur", and postmodern historical Jesus research.

  6. Partition-DFT on the Water Dimer

    CERN Document Server

    Gómez, Sara; Restrepo, Albeiro; Wasserman, Adam

    2016-01-01

    As is well known, the ground-state symmetry group of the water dimer switches from its equilibrium $C_{s}$-character to $C_{2h}$-character as the distance between the two oxygen atoms of the dimer decreases below $R_{\\rm O-O}\\sim 2.5$ \\AA{}. For a range of $R_{\\rm O-O}$ between 1 and 5 \\AA{}, and for both symmetries, we apply Partition Density Functional Theory (PDFT) to find the unique monomer densities that sum to the correct dimer densities while minimizing the sum of the monomer energies. We calculate the work involved in deforming the isolated monomer densities and find that it is slightly larger for the $C_s$ geometry for all $R_{\\rm O-O}$. We discuss how the PDFT densities and the corresponding partition potentials support the orbital-interaction picture of hydrogen-bond formation.

  7. Renal Hypodysplasia Associates with a Wnt4 Variant that Causes Aberrant Canonical Wnt Signaling

    Science.gov (United States)

    Vivante, Asaf; Mark-Danieli, Michal; Davidovits, Miriam; Harari-Steinberg, Orit; Omer, Dorit; Gnatek, Yehudit; Cleper, Roxana; Landau, Daniel; Kovalski, Yael; Weissman, Irit; Eisenstein, Israel; Soudack, Michalle; Wolf, Haike Reznik; Issler, Naomi; Lotan, Danny; Anikster, Yair

    2013-01-01

    Abnormal differentiation of the renal stem/progenitor pool into kidney tissue can lead to renal hypodysplasia (RHD), but the underlying causes of RHD are not well understood. In this multicenter study, we identified 20 Israeli pedigrees with isolated familial, nonsyndromic RHD and screened for mutations in candidate genes involved in kidney development, including PAX2, HNF1B, EYA1, SIX1, SIX2, SALL1, GDNF, WNT4, and WT1. In addition to previously reported RHD-causing genes, we found that two affected brothers were heterozygous for a missense variant in the WNT4 gene. Functional analysis of this variant revealed both antagonistic and agonistic canonical WNT stimuli, dependent on cell type. In HEK293 cells, WNT4 inhibited WNT3A induced canonical activation, and the WNT4 variant significantly enhanced this inhibition of the canonical WNT pathway. In contrast, in primary cultures of human fetal kidney cells, which maintain WNT activation and more closely represent WNT signaling in renal progenitors during nephrogenesis, this mutation caused significant loss of function, resulting in diminished canonical WNT/β-catenin signaling. In conclusion, heterozygous WNT4 variants are likely to play a causative role in renal hypodysplasia. PMID:23520208

  8. Site Partition: Turning One Site into Two for Adsorbing CO2.

    Science.gov (United States)

    Tian, Ziqi; Dai, Sheng; Jiang, De-En

    2016-07-01

    We propose the concept of site partition to explain the role of guest molecules in increasing CO2 uptake in metal-organic frameworks and to design new covalent porous materials for CO2 capture. From grand canonical Monte Carlo simulations of CO2 sorption in the recently synthesized CPM-33 MOFs, we show that guest insertion divides one open metal site into two relatively strong binding sites, hence dramatically increasing CO2 uptake. Further, we extend the site partition concept to covalent organic frameworks with large free volume. After insertion of a designed geometry-matching guest, we show that the volumetric uptake of CO2 doubles. Therefore, the concept of site partition can be used to engineer the pore space of nanoporous materials for higher gas uptake. PMID:27320252

  9. The Asian American Fakeness Canon, 1972-2002

    Science.gov (United States)

    Oishi, Eve

    2007-01-01

    The year 1972 can be seen to inaugurate not a tradition of Asian American New York theater, but the rich and multigenre collection of writing that the author has called "the Asian American fakeness canon." The fakeness canon refers to a collection of writings that take as one of their central points of reference the question of cultural and ethnic…

  10. Iterative algorithms to approximate canonical Gabor windows: Computational aspects

    DEFF Research Database (Denmark)

    Janssen, A.J.E.M; Søndergaard, Peter Lempel

    In this paper we investigate the computational aspects of some recently proposed iterative methods for approximating the canonical tight and canonical dual window of a Gabor frame (g,a,b). The iterations start with the window g while the iteration steps comprise the window g, the k^th iterand...

  11. Stability of 2nd Hilbert points of canonical curves

    CERN Document Server

    Fedorchuk, Maksym

    2011-01-01

    We establish GIT semistability of the 2nd Hilbert point of every Gieseker-Petri general canonical curve by a simple geometric argument. As a consequence, we obtain an upper bound on slopes of general families of Gorenstein curves. We also explore the question of what replaces hyperelliptic curves in the GIT quotients of the Hilbert scheme of canonical curves.

  12. Canonical connection on a class of Riemannian almost product manifolds

    CERN Document Server

    Mekerov, Dimitar

    2009-01-01

    The canonical connection on a Riemannian almost product manifolds is an analogue to the Hermitian connection on an almost Hermitian manifold. In this paper we consider the canonical connection on a class of Riemannian almost product manifolds with nonintegrable almost product structure.

  13. Critical Literature Pedagogy: Teaching Canonical Literature for Critical Literacy

    Science.gov (United States)

    Borsheim-Black, Carlin; Macaluso, Michael; Petrone, Robert

    2014-01-01

    This article introduces Critical Literature Pedagogy (CLP), a pedagogical framework for applying goals of critical literacy within the context of teaching canonical literature. Critical literacies encompass skills and dispositions to understand, question, and critique ideological messages of texts; because canonical literature is often…

  14. Canonical Quantum Teleportation of Two-Particle Arbitrary State

    Institute of Scientific and Technical Information of China (English)

    HAO Xiang; ZHU Shi-Qun

    2005-01-01

    The canonical quantum teleportation of two-particle arbitrary state is realized by means of phase operator and number operator. The maximally entangled eigenstates between the difference of phase operators and the sum of number operators are considered as the quantum channels. In contrast to the standard quantum teleportation, the different unitary local operation of canonical teleportation can be simplified by a general expression.

  15. Canonical representation for approximating solution of fuzzy polynomial equations

    Directory of Open Access Journals (Sweden)

    M. Salehnegad

    2010-06-01

    Full Text Available In this paper, the concept of canonical representation is proposed to find fuzzy roots of fuzzy polynomial equations. We transform fuzzy polynomial equations to system of crisp polynomial equations, this transformation is perform by using canonical representation based on three parameters Value, Ambiguity and Fuzziness.

  16. Improved Canonical Quantization Method of Self Dual Field

    Institute of Scientific and Technical Information of China (English)

    樊丰华; 黄永畅

    2012-01-01

    In this paper,the improved canonical quantization method of the self dual field is given in order to overcome linear combination problem about the second class constraint and the first class constraint number maximization problem in the Dirac method.In the improved canonical quantization method,there are no artificial linear combination and the first class constraint number maximization problems,at the same time,the stability of the system is considered.Therefore,the improved canonical quantization method is more natural and easier accepted by people than the usual Dirac method.We use the improved canonical quantization method to realize the canonical quantization of the self dual field,which has relation with string theory successfully and the results are equal to the results by using the Dirac method.

  17. Matrix product purifications for canonical ensembles and quantum number distributions

    Science.gov (United States)

    Barthel, Thomas

    2016-09-01

    Matrix product purifications (MPPs) are a very efficient tool for the simulation of strongly correlated quantum many-body systems at finite temperatures. When a system features symmetries, these can be used to reduce computation costs substantially. It is straightforward to compute an MPP of a grand-canonical ensemble, also when symmetries are exploited. This paper provides and demonstrates methods for the efficient computation of MPPs of canonical ensembles under utilization of symmetries. Furthermore, we present a scheme for the evaluation of global quantum number distributions using matrix product density operators (MPDOs). We provide exact matrix product representations for canonical infinite-temperature states, and discuss how they can be constructed alternatively by applying matrix product operators to vacuum-type states or by using entangler Hamiltonians. A demonstration of the techniques for Heisenberg spin-1 /2 chains explains why the difference in the energy densities of canonical and grand-canonical ensembles decays as 1 /L .

  18. Developing Key Parameters for Green Performance of Partition Wall Blocks

    Directory of Open Access Journals (Sweden)

    Goh Cheng Siew

    2016-01-01

    Full Text Available To promote sustainable construction, it is important to consider green performance of construction materials throughout the life cycle. Selecting inappropriate materials could not only affect the functional performance but also preclude the achievement of green building performance as a whole. Green performance of construction materials has therefore been one of the primary considerations of green building assessment systems. Using partition wall blocks as an example, this paper examines green performance of building materials primarily from the cradle to gate boundaries. Nine key parameters are proposed for the green performance of partition wall blocks. Apart from environmental features, technical performance of partition wall blocks is also taken into consideration since it is the determinant of the lifecycle performance. This paper offers a roadmap to decision makers to make environmentally responsible choices for their materials of internal walls and partitions, and hence provides a potential sustainable solution for green buildings.

  19. Optimal Partitioning and Granularity of Uniform Task Grkaphs

    Institute of Scientific and Technical Information of China (English)

    章中云; 李国杰

    1991-01-01

    Task partitioning is an important technique in parallel processing.In this paper,we investigate the optimal partitioning strategies and granularities of tasks with communications based on several models of parallel computer systems.Different from the usual approach,we study the optimal partitioning strategies and granularities from the viewpoint of minimizing T as well as minimizing NT2,where N is the number of processors used and T is the program execution time using N processors.Our results show that the optimal partitioning strategies for all cases discussed in this paper are the same--either to assign all tasks to one processor or to distribute them among the processors as equally as possible depending only on the functions of ratio of running time to communication time R/C.

  20. El Escritor y las Normas del Canon Literario (The Writer and the Norms of the Literary Canon).

    Science.gov (United States)

    Policarpo, Alcibiades

    This paper speculates about whether a literary canon exists in contemporary Latin American literature, particularly in the prose genre. The paper points to Carlos Fuentes, Gabriel Garcia Marquez, and Mario Vargas Llosa as the three authors who might form this traditional and liberal canon with their works "La Muerte de Artemio Cruz" (Fuentes),…

  1. Enabling grand-canonical Monte Carlo: extending the flexibility of GROMACS through the GromPy python interface module.

    Science.gov (United States)

    Pool, René; Heringa, Jaap; Hoefling, Martin; Schulz, Roland; Smith, Jeremy C; Feenstra, K Anton

    2012-05-01

    We report on a python interface to the GROMACS molecular simulation package, GromPy (available at https://github.com/GromPy). This application programming interface (API) uses the ctypes python module that allows function calls to shared libraries, for example, written in C. To the best of our knowledge, this is the first reported interface to the GROMACS library that uses direct library calls. GromPy can be used for extending the current GROMACS simulation and analysis modes. In this work, we demonstrate that the interface enables hybrid Monte-Carlo/molecular dynamics (MD) simulations in the grand-canonical ensemble, a simulation mode that is currently not implemented in GROMACS. For this application, the interplay between GromPy and GROMACS requires only minor modifications of the GROMACS source code, not affecting the operation, efficiency, and performance of the GROMACS applications. We validate the grand-canonical application against MD in the canonical ensemble by comparison of equations of state. The results of the grand-canonical simulations are in complete agreement with MD in the canonical ensemble. The python overhead of the grand-canonical scheme is only minimal.

  2. Finite Canonical Measure for Nonsingular Cosmologies

    CERN Document Server

    Page, Don N

    2011-01-01

    The total canonical (Liouville-Henneaux-Gibbons-Hawking-Stewart) measure is finite for completely nonsingular Friedmann-Robertson-Walker classical universes with a minimally coupled massive scalar field and a positive cosmological constant. For a cosmological constant very small in units of the square of the scalar field mass, most of the measure is for nearly de Sitter solutions with no inflation at a much more rapid rate. However, if one restricts to solutions in which the scalar field energy density is ever more than twice the equivalent energy density of the cosmological constant, then the number of e-folds of rapid inflation must be large, and the fraction of the measure is low in which the spatial curvature is comparable to the cosmological constant at the time when it is comparable to the energy density of the scalar field. The measure for such classical FRW-Lambda-phi models with both a big bang and a big crunch is also finite. Only the solutions with a big bang that expand forever, or the time-revers...

  3. An $OSp$ extension of Canonical Tensor Model

    CERN Document Server

    Narain, Gaurav

    2015-01-01

    Tensor models are generalizations of matrix models, and are studied as discrete models of quantum gravity for arbitrary dimensions. Among them, the canonical tensor model (CTM for short) is a rank-three tensor model formulated as a totally constrained system with a number of first-class constraints, which have a similar algebraic structure as the constraints of the ADM formalism of general relativity. In this paper, we formulate a super-extension of CTM as an attempt to incorporate fermionic degrees of freedom. The kinematical symmetry group is extended from $O(N)$ to $OSp(N,\\tilde N)$, and the constraints are constructed so that they form a first-class constraint super-Poisson algebra. This is a straightforward super-extension, and the constraints and their algebraic structure are formally unchanged from the purely bosonic case, except for the additional signs associated to the order of the fermionic indices and dynamical variables. However, this extension of CTM leads to the existence of negative norm state...

  4. Partition of polycyclic aromatic hydrocarbons on organobentonites

    Institute of Scientific and Technical Information of China (English)

    2001-01-01

    A series of organobentonites synthesized by exchanging organiccation such as dodecyltri-methylammonium (DTMA),benzyldimethyltetradecylammonium (BDTDA), cetyltrimethyl-ammonium (CTMA), octodeyltrimethylammonium (OTMA) on bentonite. The optimal condition, properties and mechanisms for the organobentonites to sorb phenanthrene, anthracene, naphthalene, acenaphthene in water were investigated in detail. The partition behavior was determined for four polycyclic aromatic hydrocarbons (PAHs), such as naphthalene, phenanthrene, anthracene and acenaphthene, from water to a series of organobentonites. The interlayer spacings and organic carbon contents of organobentonites, removal rate and sorption capacities for organobentonites to treat phenanthrene,anthracene, naphthalene, acenaphthene were correlated to the length of alkyl chains and the amounts of cation surfactant exchanged on Foundation item: the bentonite. Phenanthrene, anthracene, naphthalene, and acenaphthene sorption to organobentonites were characterized by linear isotherms, indicating solute partition between water and the organic phase composed of the large alkyl functional groups of quaternary ammonium cations. PAHs distribution coefficients (Kd)between organobentonites and water were proportional to the organic carbon contents of organobentonites. However, the partition coefficients (Koc) were nearly constants for PAHs in the system of organobentonite-water. The Koc of phenanthrene, anthracene,naphthalene, acenaphthene were 2.621x105, 2.106x105, 2.247x104,5.085x104, respectively. The means Koc values on the organobentonites are about ten to twenty times larger than the values on the soils/sediments, what is significant prerequisite for organobentonite to apply to remediation of pollution soil and groundwater. The sorption mechanism was also evaluated from octanol-water partition coefficients and aqueous solubility of PAHs. The correlations between lgKoc and 1gkow, 1gKoc and 1gS for PAHs in the system of water

  5. Canonical feature selection for joint regression and multi-class identification in Alzheimer's disease diagnosis.

    Science.gov (United States)

    Zhu, Xiaofeng; Suk, Heung-Il; Lee, Seong-Whan; Shen, Dinggang

    2016-09-01

    Fusing information from different imaging modalities is crucial for more accurate identification of the brain state because imaging data of different modalities can provide complementary perspectives on the complex nature of brain disorders. However, most existing fusion methods often extract features independently from each modality, and then simply concatenate them into a long vector for classification, without appropriate consideration of the correlation among modalities. In this paper, we propose a novel method to transform the original features from different modalities to a common space, where the transformed features become comparable and easy to find their relation, by canonical correlation analysis. We then perform the sparse multi-task learning for discriminative feature selection by using the canonical features as regressors and penalizing a loss function with a canonical regularizer. In our experiments on the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset, we use Magnetic Resonance Imaging (MRI) and Positron Emission Tomography (PET) images to jointly predict clinical scores of Alzheimer's Disease Assessment Scale-Cognitive subscale (ADAS-Cog) and Mini-Mental State Examination (MMSE) and also identify multi-class disease status for Alzheimer's disease diagnosis. The experimental results showed that the proposed canonical feature selection method helped enhance the performance of both clinical score prediction and disease status identification, outperforming the state-of-the-art methods. PMID:26254746

  6. AN APOLOGY OF THE LITERARY CANON IN A LINGUISTIC STUDY

    Directory of Open Access Journals (Sweden)

    Alexey Vladimirovich Sosnin

    2015-10-01

    Full Text Available The article highlights the principles of selecting practical material for a linguistic study aspiring to objectivity and states that in such a study orientation to the literary text is absolutely essential, as a solid corpus of literary texts is indispensable for describing complicated linguistic phenomena and mental structures standing behind them. The article puts forward the postulate that any serious study into the English language should be constructed on the English literary canon – a global textual corpus on the basis of which the greatest part of the educated speakers’ conceptual sphere is formed. At the same time, the article considers certain problems related to the Anglicist’s orientation towards the canon – its definition, limits, central and peripheral authors, the criteria of a literary work canonic status, arguments of those opposing any canonicity in literature, reconstruction of the canon in other cultures. The article also analyzes the cognitive aspect and tells about the key transformation of the English mentality, which gave rise to thinking in the terms of the time, cause-and-effect, and probability in canonic literature. The author of the article comes up with a principal conclusion: orientation to the literary canon in a linguistic study allows reconciling of linguistics and literature studies and including into the analysis nonlinguistic semiotic systems as well as idiolectal systems of conceptualizing the world in literary works.

  7. Approximation Algorithms for Submodular Multiway Partition

    CERN Document Server

    Chekuri, Chandra

    2011-01-01

    We study algorithms for the Submodular Multiway Partition problem (SubMP). An instance of SubMP consists of a finite ground set $V$, a subset of $k$ elements $S = \\{s_1,s_2,...,s_k\\}$ called terminals, and a non-negative submodular set function $f:2^V\\rightarrow \\mathbb{R}_+$ on $V$ provided as a value oracle. The goal is to partition $V$ into $k$ sets $A_1,...,A_k$ such that for $1 \\le i \\le k$, $s_i \\in A_i$ and $\\sum_{i=1}^k f(A_i)$ is minimized. SubMP generalizes some well-known problems such as the Multiway Cut problem in graphs and hypergraphs, and the Node-weighed Multiway Cut problem in graphs. SubMP for arbitrarysubmodular functions (instead of just symmetric functions) was considered by Zhao, Nagamochi and Ibaraki \\cite{ZhaoNI05}. Previous algorithms were based on greedy splitting and divide and conquer strategies. In very recent work \\cite{ChekuriE11} we proposed a convex-programming relaxation for SubMP based on the Lov\\'asz-extension of a submodular function and showed its applicability for some ...

  8. Using the Deutsch-Jozsa algorithm to partition arrays

    Science.gov (United States)

    Lipovaca, Samir

    2010-03-01

    Using the Deutsch-Jozsa algorithm, we will develop a method for solving a class of problems in which we need to determine parts of an array and then apply a specified function to each independent part. Since present quantum computers are not robust enough for code writing and execution, we will build a model of a vector quantum computer that implements the Deutsch-Jozsa algorithm from a machine language view using the APL2 programming language. The core of the method is an operator (DJBOX) which allows evaluation of an arbitrary function f by the Deutsch-Jozsa algorithm. Two key functions of the method are GET/PARTITION and CALC/WITH/PARTITIONS. The GET/PARTITION function determines parts of an array based on the function f. The CALC/WITH/PARTITIONS function determines parts of an array based on the function f and then applies another function to each independent part. We will imagine the method is implemented on the above vector quantum computer. We will show that the method can be successfully executed.

  9. High glucose modifies transient receptor potential canonical type 6 channels via increased oxidative stress and syndecan-4 in human podocytes

    DEFF Research Database (Denmark)

    Thilo, Florian; Lee, Marlene; Xia, Shengqiang;

    2014-01-01

    Transient receptor potential canonical (TRPC) channels type 6 play an important role in the function of human podocytes. Diabetic nephropathy is characterized by altered TRPC6 expression and functions of podocytes. Thus, we hypothesized that high glucose modifies TRPC6 channels via increased oxid...

  10. Sifting Function Partition for the Goldbach Problem

    OpenAIRE

    Song, Fu-Gao

    2008-01-01

    All sieve methods for the Goldbach problem sift out all the composite numbers; even though, strictly speaking, it is not necessary to do so and which is, in general, very difficult. Some new methods introduced in this paper show that the Goldbach problem can be solved under sifting out only some composite numbers. In fact, in order to prove the Goldbach conjecture, it is only necessary to show that there are prime numbers left in the residual integers after the initial sifting! This idea can ...

  11. Gentile statistics and restricted partitions

    Indian Academy of Sciences (India)

    C S Srivatsan; M V N Murthy; R K Bhaduri

    2006-03-01

    In a recent paper (Tran et al, Ann. Phys. 311, 204 (2004)), some asymptotic number theoretical results on the partitioning of an integer were derived exploiting its connection to the quantum density of states of a many-particle system. We generalise these results to obtain an asymptotic formula for the restricted or coloured partitions $p_{k}^{s} (n)$, which is the number of partitions of an integer into the summand of th powers of integers such that each power of a given integer may occur utmost times. While the method is not rigorous, it reproduces the well-known asymptotic results for = 1 apart from yielding more general results for arbitrary values of .

  12. Extremal sizes of subspace partitions

    CERN Document Server

    Heden, Olof; Nastase, Esmeralda; Sissokho, Papa

    2011-01-01

    A subspace partition $\\Pi$ of $V=V(n,q)$ is a collection of subspaces of $V$ such that each 1-dimensional subspace of $V$ is in exactly one subspace of $\\Pi$. The size of $\\Pi$ is the number of its subspaces. Let $\\sigma_q(n,t)$ denote the minimum size of a subspace partition of $V$ in which the largest subspace has dimension $t$, and let $\\rho_q(n,t)$ denote the maximum size of a subspace partition of $V$ in which the smallest subspace has dimension $t$. In this paper, we determine the values of $\\sigma_q(n,t)$ and $\\rho_q(n,t)$ for all positive integers $n$ and $t$. Furthermore, we prove that if $n\\geq 2t$, then the minimum size of a maximal partial $t$-spread in $V(n+t-1,q)$ is $\\sigma_q(n,t)$.

  13. Lattice points and simultaneous core partitions

    OpenAIRE

    Johnson, Paul

    2015-01-01

    We observe that for a and b relatively prime, the "abacus construction" identifies the set of simultaneous (a,b)-core partitions with lattice points in a rational simplex. Furthermore, many statistics on (a,b)-cores are piecewise polynomial functions on this simplex. We apply these results to rational Catalan combinatorics. Using Ehrhart theory, we reprove Anderson's theorem that there are (a+b-1)!/a!b! simultaneous (a,b)-cores, and using Euler-Maclaurin theory we prove Armstrong's conjecture...

  14. A “canonical functions” approach to the solution of two coupled differential equations of scattering theory

    OpenAIRE

    Kobeissi, H.; Fakhreddine, K.

    1991-01-01

    The system of two coupled Schrödinger differential equations (CE) arising in the close-coupling description of electron-atom scattering is considered. A “canonical functions” approach is used. This approach replaces the integration of CE for the eigenvector with unknown initial values by the integration of CE for “canonical” functions having well-defined initial values at an arbitrary origin r0(0 < r0 < ∞). The terms of the reactance matrix are then deduced from these canonical functions. The...

  15. Canonical and non-canonical barriers facing antimiR cancer therapeutics.

    Science.gov (United States)

    Cheng, Christopher J; Saltzman, W Mark; Slack, Frank J

    2013-01-01

    Once considered genetic "oddities", microRNAs (miRNAs) are now recognized as key epigenetic regulators of numerous biological processes, including some with a causal link to the pathogenesis, maintenance, and treatment of cancer. The crux of small RNA-based therapeutics lies in the antagonism of potent cellular targets; the main shortcoming of the field in general, lies in ineffective delivery. Inhibition of oncogenic miRNAs is a relatively nascent therapeutic concept, but as with predecessor RNA-based therapies, success hinges on delivery efficacy. This review will describes the canonical (e.g. pharmacokinetics and clearance, cellular uptake, endosome escape, etc.) and non-canonical (e.g. spatial localization and accessibility of miRNA, technical limitations of miRNA inhibition, off-target impacts, etc.) challenges to the delivery of antisense-based anti-miRNA therapeutics (i.e. antimiRs) for the treatment of cancer. Emphasis will be placed on how the current leading antimiR platforms-ranging from naked chemically modified oligonucleotides to nanoscale delivery vehicles-are affected by and overcome these barriers. The perplexity of antimiR delivery presents both engineering and biological hurdles that must be overcome in order to capitalize on the extensive pharmacological benefits of antagonizing tumor-associated miRNAs.

  16. Beta-Negative Binomial Process and Exchangeable Random Partitions for Mixed-Membership Modeling

    OpenAIRE

    Zhou, Mingyuan

    2014-01-01

    The beta-negative binomial process (BNBP), an integer-valued stochastic process, is employed to partition a count vector into a latent random count matrix. As the marginal probability distribution of the BNBP that governs the exchangeable random partitions of grouped data has not yet been developed, current inference for the BNBP has to truncate the number of atoms of the beta process. This paper introduces an exchangeable partition probability function to explicitly describe how the BNBP clu...

  17. The Partition Ensemble Fallacy Fallacy

    CERN Document Server

    Nemoto, K; Nemoto, Kae; Braunstein, Samuel L.

    2002-01-01

    The Partition Ensemble Fallacy was recently applied to claim no quantum coherence exists in coherent states produced by lasers. We show that this claim relies on an untestable belief of a particular prior distribution of absolute phase. One's choice for the prior distribution for an unobservable quantity is a matter of `religion'. We call this principle the Partition Ensemble Fallacy Fallacy. Further, we show an alternative approach to construct a relative-quantity Hilbert subspace where unobservability of certain quantities is guaranteed by global conservation laws. This approach is applied to coherent states and constructs an approximate relative-phase Hilbert subspace.

  18. Pyrcca: regularized kernel canonical correlation analysis in Python and its applications to neuroimaging

    OpenAIRE

    Bilenko, Natalia Y.; Gallant, Jack L.

    2015-01-01

    Canonical correlation analysis (CCA) is a valuable method for interpreting cross-covariance across related datasets of different dimensionality. There are many potential applications of CCA to neuroimaging data analysis. For instance, CCA can be used for finding functional similarities across fMRI datasets collected from multiple subjects without resampling individual datasets to a template anatomy. In this paper, we introduce Pyrcca, an open-source Python module for executing CCA between two...

  19. The canonical Cartan bundle and connection in CR geometry

    OpenAIRE

    Herzlich, Marc

    2009-01-01

    minor changes ; wrong author in reference [7] corrected; International audience; We give a differential geometric description of the Cartan (or tractor) bundle and its canonical connection in CR geometry, thus offering a direct, alternative, definition to the usual abstract approach.

  20. Kerr black hole in canonically deformed space-time

    CERN Document Server

    Daszkiewicz, Marcin

    2014-01-01

    We investigate the Kerr black hole defined on canonically deformed space-time. Particulary, we find the corresponding event horizon, the ergosphere, the temperature and the entropy of such deformed object.

  1. Asymptotic distributions in the projection pursuit based canonical correlation analysis

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    In this paper, associations between two sets of random variables based on the projection pursuit (PP) method are studied. The asymptotic normal distributions of estimators of the PP based canonical correlations and weighting vectors are derived.

  2. CANONICAL CORRELATION ANALYSIS BETWEEN TIME SERIES AND STATIC OUTCOMES, WITH APPLICATION TO THE SPECTRAL ANALYSIS OF HEART RATE VARIABILITY.

    Science.gov (United States)

    Krafty, Robert T; Hall, Martica

    2013-03-01

    Although many studies collect biomedical time series signals from multiple subjects, there is a dearth of models and methods for assessing the association between frequency domain properties of time series and other study outcomes. This article introduces the random Cramér representation as a joint model for collections of time series and static outcomes where power spectra are random functions that are correlated with the outcomes. A canonical correlation analysis between cepstral coefficients and static outcomes is developed to provide a flexible yet interpretable measure of association. Estimates of the canonical correlations and weight functions are obtained from a canonical correlation analysis between the static outcomes and maximum Whittle likelihood estimates of truncated cepstral coefficients. The proposed methodology is used to analyze the association between the spectrum of heart rate variability and measures of sleep duration and fragmentation in a study of older adults who serve as the primary caregiver for their ill spouse.

  3. CANONICAL CORRELATION ANALYSIS BETWEEN TIME SERIES AND STATIC OUTCOMES, WITH APPLICATION TO THE SPECTRAL ANALYSIS OF HEART RATE VARIABILITY.

    Science.gov (United States)

    Krafty, Robert T; Hall, Martica

    2013-03-01

    Although many studies collect biomedical time series signals from multiple subjects, there is a dearth of models and methods for assessing the association between frequency domain properties of time series and other study outcomes. This article introduces the random Cramér representation as a joint model for collections of time series and static outcomes where power spectra are random functions that are correlated with the outcomes. A canonical correlation analysis between cepstral coefficients and static outcomes is developed to provide a flexible yet interpretable measure of association. Estimates of the canonical correlations and weight functions are obtained from a canonical correlation analysis between the static outcomes and maximum Whittle likelihood estimates of truncated cepstral coefficients. The proposed methodology is used to analyze the association between the spectrum of heart rate variability and measures of sleep duration and fragmentation in a study of older adults who serve as the primary caregiver for their ill spouse. PMID:24851143

  4. On Uncertainty Principle for Quaternionic Linear Canonical Transform

    Directory of Open Access Journals (Sweden)

    Kit Ian Kou

    2013-01-01

    Full Text Available We generalize the linear canonical transform (LCT to quaternion-valued signals, known as the quaternionic linear canonical transform (QLCT. Using the properties of the LCT we establish an uncertainty principle for the QLCT. This uncertainty principle prescribes a lower bound on the product of the effective widths of quaternion-valued signals in the spatial and frequency domains. It is shown that only a 2D Gaussian signal minimizes the uncertainty.

  5. Using lattice methods in non-canonical quantum statistics

    International Nuclear Information System (INIS)

    We define a natural coarse-graining procedure which can be applied to any closed equilibrium quantum system described by a density matrix ensemble and we show how the coarse-graining leads to the Gaussian and canonical ensembles. After this motivation, we present two ways of evaluating the Gaussian expectation values with lattice simulations. The first one is computationally demanding but general, whereas the second employs only canonical expectation values but it is applicable only for systems which are almost thermodynamical

  6. Partitioning of Nanoparticles into Organic Phases and Model Cells

    Energy Technology Data Exchange (ETDEWEB)

    Posner, J.D.; Westerhoff, P.; Hou, W-C.

    2011-08-25

    dissolved substances" or "more like colloids" as the division between behaviors of macromolecules versus colloids remains ill-defined. Below we detail our work on two broadly defined objectives: (i) Partitioning of ENP into octanol, lipid bilayer, and water, and (ii) disruption of lipid bilayers by ENPs. We have found that the partitioning of NP reaches pseudo-equilibrium distributions between water and organic phases. The equilibrium partitioning most strongly depends on the particle surface charge, which leads us to the conclusion that electrostatic interactions are critical to understanding the fate of NP in the environment. We also show that the kinetic rate at which particle partition is a function of their size (small particles partition faster by number) as can be predicted from simple DLVO models. We have found that particle number density is the most effective dosimetry to present our results and provide quantitative comparison across experiments and experimental platforms. Cumulatively, our work shows that lipid bilayers are a more effective organic phase than octanol because of the definable surface area and ease of interpretation of the results. Our early comparison of NP partitioning between water and lipids suggest that this measurement can be predictive of bioaccumulation in aquatic organisms. We have shown that nanoparticle disrupt lipid bilayer membranes and detail how NP-bilayer interaction leads to the malfunction of lipid bilayers in regulating the fluxes of ionic charges and molecules. Our results show that the disruption of the lipid membranes is similar to that of toxin melittin, except single particles can disrupt a bilayer. We show that only a single particle is required to disrupt a 150 nm DOPC liposome. The equilibrium leakage of membranes is a function of the particle number density and particle surface charge, consistent with results from our partitioning experiments. Our disruption experiments with varying surface functionality show that

  7. Assimilate Partitioning and Plant Development

    Institute of Scientific and Technical Information of China (English)

    Yong-Ling Ruan; John W.Patrick; Hans Weber

    2010-01-01

    @@ It has been a pleasure to organize this special issue of Molecular Plant on 'Assimilate Partitioning and Plant Development'. Assimilate, a collective term describing organic carbon (C) and nitrogen (N), is of paramount importance for plant development and realization of crop productivity.

  8. Canonical quantization of a string describing N branes at angles

    Energy Technology Data Exchange (ETDEWEB)

    Pesando, Igor, E-mail: ipesando@to.infn.it

    2014-12-15

    We study the canonical quantization of a bosonic string in presence of N twist fields. This generalizes the quantization of the twisted string in two ways: the in and out states are not necessarily twisted and the number of twist fields N can be bigger than 2. In order to quantize the theory we need to find the normal modes. Then we need to define a product between two modes which is conserved. Because of this we need to use the Klein–Gordon product and to separate the string coordinate into the classical and the quantum part. The quantum part has different boundary conditions than the original string coordinates but these boundary conditions are precisely those which make the operator describing the equation of motion self adjoint. The splitting of the string coordinates into a classical and quantum part allows the formulation of an improved overlap principle. Using this approach we then proceed in computing the generating function for the generic correlator with L untwisted operators and N (excited) twist fields for branes at angles. We recover as expected the results previously obtained using the path integral. This construction explains why these correlators are given by a generalization of the Wick theorem.

  9. A canonical circuit for generating phase-amplitude coupling.

    Science.gov (United States)

    Onslow, Angela C E; Jones, Matthew W; Bogacz, Rafal

    2014-01-01

    'Phase amplitude coupling' (PAC) in oscillatory neural activity describes a phenomenon whereby the amplitude of higher frequency activity is modulated by the phase of lower frequency activity. Such coupled oscillatory activity--also referred to as 'cross-frequency coupling' or 'nested rhythms'--has been shown to occur in a number of brain regions and at behaviorally relevant time points during cognitive tasks; this suggests functional relevance, but the circuit mechanisms of PAC generation remain unclear. In this paper we present a model of a canonical circuit for generating PAC activity, showing how interconnected excitatory and inhibitory neural populations can be periodically shifted in to and out of oscillatory firing patterns by afferent drive, hence generating higher frequency oscillations phase-locked to a lower frequency, oscillating input signal. Since many brain regions contain mutually connected excitatory-inhibitory populations receiving oscillatory input, the simplicity of the mechanism generating PAC in such networks may explain the ubiquity of PAC across diverse neural systems and behaviors. Analytic treatment of this circuit as a nonlinear dynamical system demonstrates how connection strengths and inputs to the populations can be varied in order to change the extent and nature of PAC activity, importantly which phase of the lower frequency rhythm the higher frequency activity is locked to. Consequently, this model can inform attempts to associate distinct types of PAC with different network topologies and physiologies in real data. PMID:25136855

  10. Canon multifunction copier machines – now with onsite support!

    CERN Multimedia

    2013-01-01

    Following a retendering process in 2012, the IT Department is pleased to announce that leased multifunction copier machines are now covered by onsite support, provided by Canon technicians via the CERN Service Desk support system.   You can now contact the Service Desk regarding any problems or requests for toner: Telephone: 77777 Email: Service-Desk@cern.ch Please remember to quote the machine printer name and/or serial number (marked on the side of the machine). The following submission forms are available online: Report a failure with a printer or copier Request for network printer or copier installation or move Request toner/ink for my printer or copier The website below details the range of models available, all of which include print, photocopy and scan-to-mail functions as standard. These multifunction copier machines are leased subject to a monthly charge (minimum of 48 months) plus a “per click” charge to cover consumables (except staples), leaving you noth...

  11. Revised Canonical Quantum Gravity via the Frame Fixing

    CERN Document Server

    Mercuri, S; Mercuri, Simone; Montani, Giovanni

    2004-01-01

    We present a new reformulation of the canonical quantum geometrodynamics, which allows to overcome the fundamental problem of the frozen formalism and, therefore, to construct an appropriate Hilbert space associate to the solution of the restated dynamics. More precisely, to remove the ambiguity contained in the Wheeler-DeWitt approach, with respect to the possibility of a (3 + 1)-splitting when the space-time is in a quantum regime, we fix the reference frame (i.e. the lapse function and the shift vector) by introducing the so-called kinematical action; as a consequence the new super-Hamiltonian constraint becomes a parabolic one and we arrive to a Schroedinger-like approach for the quantum dynamics. In the semiclassical limit our theory provides General Relativity in the presence of an additional energy-momentum density contribution coming from no longer zero eigenvalues of the Hamiltonian constraints; the interpretation of these new contributions comes out in natural way as soon as it is recognized that th...

  12. Time Reversal and n-qubit Canonical Decompositions

    CERN Document Server

    Bullock, S S; O'Leary, D P; Bullock, Stephen S.; Brennen, Gavin K.; Leary, Dianne P. O'; Bullock, Stephen S.; Brennen, Gavin K.; Leary, Dianne P. O'

    2004-01-01

    For n an even number of qubits and v a unitary evolution, a matrix decomposition v=k1 a k2 of the unitary group is explicitly computable and allows for study of the dynamics of the concurrence entanglement monotone. The side factors k1 and k2 of this Concurrence Canonical Decomposition (CCD) are concurrence symmetries, so the dynamics reduce to consideration of the a factor. In this work, we provide an explicit numerical algorithm computing v=k1 a k2 for n odd. Further, in the odd case we lift the monotone to a two-argument function, allowing for a theory of concurrence dynamics in odd qubits. The generalization may also be studied using the CCD, leading again to maximal concurrence capacity for most unitaries. The key technique is to consider the spin-flip as a time reversal symmetry operator in Wigner's axiomatization; the original CCD derivation may be restated entirely in terms of this time reversal. En route, we observe a Kramers' nondegeneracy: the existence of a nondegenerate eigenstate of any time rev...

  13. Ligand-Independent Canonical Wnt Activity in Canine Mammary Tumor Cell Lines Associated with Aberrant LEF1 Expression

    Science.gov (United States)

    van Wolferen, Monique E.; Rao, Nagesha A. S.; Grizelj, Juraj; Vince, Silvijo; Hellmen, Eva; Mol, Jan A.

    2014-01-01

    Pet dogs very frequently develop spontaneous mammary tumors and have been suggested as a good model organism for breast cancer research. In order to obtain an insight into underlying signaling mechanisms during canine mammary tumorigenesis, in this study we assessed the incidence and the mechanism of canonical Wnt activation in a panel of 12 canine mammary tumor cell lines. We show that a subset of canine mammary cell lines exhibit a moderate canonical Wnt activity that is dependent on Wnt ligands, similar to what has been described in human breast cancer cell lines. In addition, three of the tested canine mammary cell lines have a high canonical Wnt activity that is not responsive to inhibitors of Wnt ligand secretion. Tumor cell lines with highly active canonical Wnt signaling often carry mutations in key members of the Wnt signaling cascade. These cell lines, however, carry no mutations in the coding regions of intracellular Wnt pathway components (APC, β-catenin, GSK3β, CK1α and Axin1) and have a functional β-catenin destruction complex. Interestingly, however, the cell lines with high canonical Wnt activity specifically overexpress LEF1 mRNA and the knock-down of LEF1 significantly inhibits TCF-reporter activity. In addition, LEF1 is overexpressed in a subset of canine mammary carcinomas, implicating LEF1 in ligand-independent activation of canonical Wnt signaling in canine mammary tumors. We conclude that canonical Wnt activation may be a frequent event in canine mammary tumors both through Wnt ligand-dependent and novel ligand–independent mechanisms. PMID:24887235

  14. Ligand-independent canonical Wnt activity in canine mammary tumor cell lines associated with aberrant LEF1 expression.

    Directory of Open Access Journals (Sweden)

    Ana Gracanin

    Full Text Available Pet dogs very frequently develop spontaneous mammary tumors and have been suggested as a good model organism for breast cancer research. In order to obtain an insight into underlying signaling mechanisms during canine mammary tumorigenesis, in this study we assessed the incidence and the mechanism of canonical Wnt activation in a panel of 12 canine mammary tumor cell lines. We show that a subset of canine mammary cell lines exhibit a moderate canonical Wnt activity that is dependent on Wnt ligands, similar to what has been described in human breast cancer cell lines. In addition, three of the tested canine mammary cell lines have a high canonical Wnt activity that is not responsive to inhibitors of Wnt ligand secretion. Tumor cell lines with highly active canonical Wnt signaling often carry mutations in key members of the Wnt signaling cascade. These cell lines, however, carry no mutations in the coding regions of intracellular Wnt pathway components (APC, β-catenin, GSK3β, CK1α and Axin1 and have a functional β-catenin destruction complex. Interestingly, however, the cell lines with high canonical Wnt activity specifically overexpress LEF1 mRNA and the knock-down of LEF1 significantly inhibits TCF-reporter activity. In addition, LEF1 is overexpressed in a subset of canine mammary carcinomas, implicating LEF1 in ligand-independent activation of canonical Wnt signaling in canine mammary tumors. We conclude that canonical Wnt activation may be a frequent event in canine mammary tumors both through Wnt ligand-dependent and novel ligand-independent mechanisms.

  15. Inversion of hematocrit partition at microfluidic bifurcations.

    Science.gov (United States)

    Shen, Zaiyi; Coupier, Gwennou; Kaoui, Badr; Polack, Benoît; Harting, Jens; Misbah, Chaouqi; Podgorski, Thomas

    2016-05-01

    Partitioning of red blood cells (RBCs) at the level of bifurcations in the microcirculatory system affects many physiological functions yet it remains poorly understood. We address this problem by using T-shaped microfluidic bifurcations as a model. Our computer simulations and in vitro experiments reveal that the hematocrit (ϕ0) partition depends strongly on RBC deformability, as long as ϕ0<20% (within the normal range in microcirculation), and can even lead to complete deprivation of RBCs in a child branch. Furthermore, we discover a deviation from the Zweifach-Fung effect which states that the child branch with lower flow rate recruits less RBCs than the higher flow rate child branch. At small enough ϕ0, we get the inverse scenario, and the hematocrit in the lower flow rate child branch is even higher than in the parent vessel. We explain this result by an intricate up-stream RBC organization and we highlight the extreme dependence of RBC transport on geometrical and cell mechanical properties. These parameters can lead to unexpected behaviors with consequences on the microcirculatory function and oxygen delivery in healthy and pathological conditions.

  16. On free fermions and plane partitions

    OpenAIRE

    Foda, O.; Wheeler, M.; Zuparic, M.

    2008-01-01

    We use free fermion methods to re-derive a result of Okounkov and Reshetikhin relating charged fermions to random plane partitions, and to extend it to relate neutral fermions to strict plane partitions.

  17. On Packing Densities of Set Partitions

    OpenAIRE

    Goyt, Adam M.; Pudwell, Lara K.

    2013-01-01

    We study packing densities for set partitions, which is a generalization of packing words. We use results from the literature about packing densities for permutations and words to provide packing densities for set partitions. These results give us most of the packing densities for partitions of the set $\\{1,2,3\\}$. In the final section we determine the packing density of the set partition $\\{\\{1,3\\},\\{2\\}\\}$.

  18. Effects of Sequence Partitioning on Compression Rate

    OpenAIRE

    Alagoz, B. Baykant

    2010-01-01

    In the paper, a theoretical work is done for investigating effects of splitting data sequence into packs of data set. We proved that a partitioning of data sequence is possible to find such that the entropy rate at each subsequence is lower than entropy rate of the source. Effects of sequence partitioning on overall compression rate are argued on the bases of partitioning statistics, and then, an optimization problem for an optimal partition is defined to improve overall compression rate of a...

  19. Non-Canonical EZH2 Transcriptionally Activates RelB in Triple Negative Breast Cancer

    Science.gov (United States)

    Lawrence, Cortney L.; Baldwin, Albert S.

    2016-01-01

    Enhancer of zeste homology 2 (EZH2) is the methyltransferase component of the polycomb repressive complex (PRC2) which represses gene transcription via histone H3 trimethylation at lysine 23 (H3K27me3). EZH2 activity has been linked with oncogenesis where it is thought to block expression of certain tumor suppressors. Relative to a role in cancer, EZH2 functions to promote self-renewal and has been shown to be important for the tumor-initiating cell (TIC) phenotype in breast cancer. Recently a non-canonical role for EZH2 has been identified where it promotes transcriptional activation of certain genes. Here we show that EZH2, through a methyltransferase-independent mechanism, promotes the transcriptional activation of the non-canonical NF-κB subunit RelB to drive self-renewal and the TIC phenotype of triple-negative breast cancer cells. PMID:27764181

  20. Nitrogen removal and microbial characteristics in CANON biofilters fed with different ammonia levels.

    Science.gov (United States)

    Liang, Yuhai; Li, Dong; Zhang, Xiaojing; Zeng, Huiping; Yang, Zhuo; Cui, Shaoming; Zhang, Jie

    2014-11-01

    The nitrogen removal performance and microbial characteristics of four completely autotrophic nitrogen removal over nitrite (CANON) biofilters were investigated. These four reactors were simultaneously seeded from a stable CANON biofilter with a seeding ratio of 1:1, which were fed with different ammonia levels. Results suggested that with the ammonia of 200-400 mg L(-1), aerobic ammonia-oxidizing bacteria (AerAOB) and anaerobic ammonia-oxidizing bacteria (AnAOB) could perform harmonious work. The bioactivity and population of the two groups of bacteria were both high, which then resulted in excellent nitrogen removal, while too low or too high ammonia would both lead to worse performance. When ammonia was too high, the bioactivity, biodiversity and population of AerAOB all decreased and then resulted in the lowest nitrogen removal. Nitrosomonas and Candidatus Brocadia were detected as predominant functional microbes in all the four reactors. Finally, strategies for treating sewage with different ammonia levels were proposed.

  1. Quantisation, Representation and Reduction; How Should We Interpret the Quantum Hamiltonian Constraints of Canonical Gravity?

    Directory of Open Access Journals (Sweden)

    Karim P. Y. Thébault

    2011-03-01

    Full Text Available Hamiltonian constraints feature in the canonical formulation of general relativity. Unlike typical constraints they cannot be associated with a reduction procedure leading to a non-trivial reduced phase space and this means the physical interpretation of their quantum analogues is ambiguous. In particular, can we assume that “quantisation commutes with reduction” and treat the promotion of these constraints to operators annihilating the wave function, according to a Dirac type procedure, as leading to a Hilbert space equivalent to that reached by quantisation of the problematic reduced space? If not, how should we interpret Hamiltonian constraints quantum mechanically? And on what basis do we assert that quantisation and reduction commute anyway? These questions will be refined and explored in the context of modern approaches to the quantisation of canonical general relativity.

  2. Quantisation, Representation and Reduction; How Should We Interpret the Quantum Hamiltonian Constraints of Canonical Gravity?

    CERN Document Server

    Thebault, Karim P Y

    2011-01-01

    Hamiltonian constraints feature in the canonical formulation of general relativity. Unlike typical constraints they cannot be associated with a reduction procedure leading to a non-trivial reduced phase space and this means the physical interpretation of their quantum analogues is ambiguous. In particular, can we assume that `quantisation commutes with reduction' and treat the promotion of these constraints to operators annihilating the wave function, according to a Dirac type procedure, as leading to a Hilbert space equivalent to that reached by quantisation of the problematic reduced space? If not, how should we interpret Hamiltonian constraints quantum mechanically? And on what basis do we assert that quantisation and reduction commute anyway? These questions will be refined and explored in the context of modern approaches to the quantisation of canonical general relativity.

  3. Canonical quantization of macroscopic electrodynamics in a linear, inhomogeneous magneto-electric medium

    CERN Document Server

    Judge, A C; Sipe, J E; de Sterke, C M

    2012-01-01

    We present a canonical quantization of macroscopic electrodynamics. The results apply to inhomogeneous media with a broad class of linear magneto-electric responses which are consistent with the Kramers-Kronig and Onsager relations. Through its ability to accommodate strong dispersion and loss, our theory provides a rigorous foundation for the study of quantum optical processes in structures incorporating metamaterials, provided these may be modeled as magneto-electric media. Previous canonical treatments of dielectric and magneto-dielectric media have expressed the electromagnetic field operators in either a Green function or mode expansion representation. Here we present our results in the mode expansion picture with a view to applications in guided wave and cavity quantum optics.

  4. On a canonical quantization of 3D Anti de Sitter pure gravity

    Science.gov (United States)

    Kim, Jihun; Porrati, Massimo

    2015-10-01

    We perform a canonical quantization of pure gravity on AdS 3 using as a technical tool its equivalence at the classical level with a Chern-Simons theory with gauge group SL(2,{R})× SL(2,{R}) . We first quantize the theory canonically on an asymptotically AdS space -which is topologically the real line times a Riemann surface with one connected boundary. Using the "constrain first" approach we reduce canonical quantization to quantization of orbits of the Virasoro group and Kähler quantization of Teichmüller space. After explicitly computing the Kähler form for the torus with one boundary component and after extending that result to higher genus, we recover known results, such as that wave functions of SL(2,{R}) Chern-Simons theory are conformal blocks. We find new restrictions on the Hilbert space of pure gravity by imposing invariance under large diffeomorphisms and normalizability of the wave function. The Hilbert space of pure gravity is shown to be the target space of Conformal Field Theories with continuous spectrum and a lower bound on operator dimensions. A projection defined by topology changing amplitudes in Euclidean gravity is proposed. It defines an invariant subspace that allows for a dual interpretation in terms of a Liouville CFT. Problems and features of the CFT dual are assessed and a new definition of the Hilbert space, exempt from those problems, is proposed in the case of highly-curved AdS 3.

  5. On a Canonical Quantization of 3D Anti de Sitter Pure Gravity

    CERN Document Server

    Kim, Jihun

    2015-01-01

    We perform a canonical quantization of pure gravity on AdS3 using as a technical tool its equivalence at the classical level with a Chern-Simons theory with gauge group SL(2,R)xSL(2,R). We first quantize the theory canonically on an asymptotically AdS space --which is topologically the real line times a Riemann surface with one connected boundary. Using the "constrain first" approach we reduce canonical quantization to quantization of orbits of the Virasoro group and Kaehler quantization of Teichmuller space. After explicitly computing the Kaehler form for the torus with one boundary component and after extending that result to higher genus, we recover known results, such as that wave functions of SL(2,R) Chern-Simons theory are conformal blocks. We find new restrictions on the Hilbert space of pure gravity by imposing invariance under large diffeomorphisms and normalizability of the wave function. The Hilbert space of pure gravity is shown to be the target space of Conformal Field Theories with continuous sp...

  6. Solving set partitioning problems using lagrangian relaxation

    NARCIS (Netherlands)

    van Krieken, M.G.C.

    2006-01-01

    This thesis focuses on the set partitioning problem. Given a collection of subsets of a certain root set and costs associated to these subsets, the set partitioning problem is the problem of finding a minimum cost partition of the root set. Many real-life problems, such as vehicle routing and crew s

  7. Components of the canonical and non-canonical Wnt pathways are not mis-expressed in pituitary tumors.

    Directory of Open Access Journals (Sweden)

    Leandro Machado Colli

    Full Text Available INTRODUCTION: Canonical and non-canonical Wnt pathways are involved in the genesis of multiple tumors; however, their role in pituitary tumorigenesis is mostly unknown. OBJECTIVE: This study evaluated gene and protein expression of Wnt pathways in pituitary tumors and whether these expression correlate to clinical outcome. MATERIALS AND METHODS: Genes of the WNT canonical pathway: activating ligands (WNT11, WNT4, WNT5A, binding inhibitors (DKK3, sFRP1, β-catenin (CTNNB1, β-catenin degradation complex (APC, AXIN1, GSK3β, inhibitor of β-catenin degradation complex (AKT1, sequester of β-catenin (CDH1, pathway effectors (TCF7, MAPK8, NFAT5, pathway mediators (DVL-1, DVL-2, DVL-3, PRICKLE, VANGL1, target genes (MYB, MYC, WISP2, SPRY1, TP53, CCND1; calcium dependent pathway (PLCB1, CAMK2A, PRKCA, CHP; and planar cell polarity pathway (PTK7, DAAM1, RHOA were evaluated by QPCR, in 19 GH-, 18 ACTH-secreting, 21 non-secreting (NS pituitary tumors, and 5 normal pituitaries. Also, the main effectors of canonical (β-catenin, planar cell polarity (JNK, and calcium dependent (NFAT5 Wnt pathways were evaluated by immunohistochemistry. RESULTS: There are no differences in gene expression of canonical and non-canonical Wnt pathways between all studied subtypes of pituitary tumors and normal pituitaries, except for WISP2, which was over-expressed in ACTH-secreting tumors compared to normal pituitaries (4.8x; p = 0.02, NS pituitary tumors (7.7x; p = 0.004 and GH-secreting tumors (5.0x; p = 0.05. β-catenin, NFAT5 and JNK proteins showed no expression in normal pituitaries and in any of the pituitary tumor subtypes. Furthermore, no association of the studied gene or protein expression was observed with tumor size, recurrence, and progressive disease. The hierarchical clustering showed a regular pattern of genes of the canonical and non-canonical Wnt pathways randomly distributed throughout the dendrogram. CONCLUSIONS: Our data reinforce previous reports

  8. New Multiple Soliton-like and Periodic Solutions for (2+1)-Dimensional Canonical Generalized KP Equation with Variable Coefficients

    Institute of Scientific and Technical Information of China (English)

    ZHANG Li-Hua; LIU Xi-Qiang; BAI Cheng-Lin

    2006-01-01

    In this paper, the generalized tanh function method is extended to (2+1)-dimensional canonical generalized KP (CGKP) equation with variable coefficients. Taking advantage of the Riccati equation, many explicit exact solutions,which contain multiple soliton-like and periodic solutions, are obtained for the (2+1)-dimensional CGKP equation with variable coefficients.

  9. On Markov chains induced by partitioned transition probability matrices

    OpenAIRE

    Kaijser, Thomas

    2009-01-01

    Let S be a denumerable state space and let P be a transition probability matrix on S. If a denumerable set M of nonnegative matrices is such that the sum of the matrices is equal to P, then we call M a partition of P. Let K denote the set of probability vectors on S. To every partition M of P we can associate a transition probability function on K defined in such a way that if p in K and m in M are such that ||pm|| > 0, then, with probability ||pm|| the vector p is transferred to the vector p...

  10. Orientation and velocity dependence of the nonequilibrium partition coefficient

    Science.gov (United States)

    Beatty, K. M.; Jackson, K. A.

    1995-01-01

    Monte Carlo simulations based on a Spin-1 Ising Model for binary alloys have been used to investigate the non-equilibrium partition coefficient (k(sub neq)) as a function of solid-liquid interface velocity and orientation. In simulations of Si with a second component k(sub neq) is greater in the [111] direction than the [100] direction in agreement with experimental results reported by Azlz et al. The simulated partition coefficient scales with the square of the step velocity divided by the diffusion coefficient of the secondary component in the liquid.

  11. Lex-Partitioning: A New Option for BDD Search

    Directory of Open Access Journals (Sweden)

    Stefan Edelkamp

    2012-10-01

    Full Text Available For the exploration of large state spaces, symbolic search using binary decision diagrams (BDDs can save huge amounts of memory and computation time. State sets are represented and modified by accessing and manipulating their characteristic functions. BDD partitioning is used to compute the image as the disjunction of smaller subimages. In this paper, we propose a novel BDD partitioning option. The partitioning is lexicographical in the binary representation of the states contained in the set that is represented by a BDD and uniform with respect to the number of states represented. The motivation of controlling the state set sizes in the partitioning is to eventually bridge the gap between explicit and symbolic search. Let n be the size of the binary state vector. We propose an O(n ranking and unranking scheme that supports negated edges and operates on top of precomputed satcount values. For the uniform split of a BDD, we then use unranking to provide paths along which we partition the BDDs. In a shared BDD representation the efforts are O(n. The algorithms are fully integrated in the CUDD library and evaluated in strongly solving general game playing benchmarks.

  12. Activation of the Canonical Wnt Signaling Pathway Induces Cementum Regeneration.

    Science.gov (United States)

    Han, Pingping; Ivanovski, Saso; Crawford, Ross; Xiao, Yin

    2015-07-01

    Canonical Wnt signaling is important in tooth development but it is unclear whether it can induce cementogenesis and promote the regeneration of periodontal tissues lost because of disease. Therefore, the aim of this study is to investigate the influence of canonical Wnt signaling enhancers on human periodontal ligament cell (hPDLCs) cementogenic differentiation in vitro and cementum repair in a rat periodontal defect model. Canonical Wnt signaling was induced by (1) local injection of lithium chloride; (2) local injection of sclerostin antibody; and (3) local injection of a lentiviral construct overexpressing β-catenin. The results showed that the local activation of canonical Wnt signaling resulted in significant new cellular cementum deposition and the formation of well-organized periodontal ligament fibers, which was absent in the control group. In vitro experiments using hPDLCs showed that the Wnt signaling pathway activators significantly increased mineralization, alkaline phosphatase (ALP) activity, and gene and protein expression of the bone and cementum markers osteocalcin (OCN), osteopontin (OPN), cementum protein 1 (CEMP1), and cementum attachment protein (CAP). Our results show that the activation of the canonical Wnt signaling pathway can induce in vivo cementum regeneration and in vitro cementogenic differentiation of hPDLCs. PMID:25556853

  13. Graph partitioning advance clustering technique

    CERN Document Server

    Madhulatha, T Soni

    2012-01-01

    Clustering is a common technique for statistical data analysis, Clustering is the process of grouping the data into classes or clusters so that objects within a cluster have high similarity in comparison to one another, but are very dissimilar to objects in other clusters. Dissimilarities are assessed based on the attribute values describing the objects. Often, distance measures are used. Clustering is an unsupervised learning technique, where interesting patterns and structures can be found directly from very large data sets with little or none of the background knowledge. This paper also considers the partitioning of m-dimensional lattice graphs using Fiedler's approach, which requires the determination of the eigenvector belonging to the second smallest Eigenvalue of the Laplacian with K-means partitioning algorithm.

  14. Ontology Partitioning: Clustering Based Approach

    Directory of Open Access Journals (Sweden)

    Soraya Setti Ahmed

    2015-05-01

    Full Text Available The semantic web goal is to share and integrate data across different domains and organizations. The knowledge representations of semantic data are made possible by ontology. As the usage of semantic web increases, construction of the semantic web ontologies is also increased. Moreover, due to the monolithic nature of the ontology various semantic web operations like query answering, data sharing, data matching, data reuse and data integration become more complicated as the size of ontology increases. Partitioning the ontology is the key solution to handle this scalability issue. In this work, we propose a revision and an enhancement of K-means clustering algorithm based on a new semantic similarity measure for partitioning given ontology into high quality modules. The results show that our approach produces meaningful clusters than the traditional algorithm of K-means.

  15. A partitioned central solar receiver

    International Nuclear Information System (INIS)

    Else of solar energy as substitute for conventional fuels at a competitive cost requires efficient conversion from solar radiation to usable forms of energy. In solar thermal or thermochemical applications, high efficiency usually re- quires high temperature and high concentration of incoming radiation. The main form of energy loss from high temperature solar central receivers is thermal emission ('re radiation'), at an effective temperature close to the maximum receiver temperature. This loss is reduced if the aperture is divided into segments, most of which are maintained at lower temperatures. A two-stage partitioned receiver demonstrating this concept is under construction at the Weizman Solar Tower. The high-temperature stage is the DIAPR (Directly Irradiated Annular Pressurized Receiver). The low-temperature stage is made of tubular cavity receivers of simpler design. Preliminary optical and thermal design of the partitioned receiver is presented. For the design exit temperature of 1500 K, the aperture size of the partitioned receiver is about 60% of the equivalent single-stage receiver, indicating a significant increase of conversion efficiency. The exit temperature of the low-temperature stage is around 1100 K, allowing simpler design and inexpensive construction. (authors)

  16. Ferrous iron partitioning in the lower mantle

    Science.gov (United States)

    Muir, Joshua M. R.; Brodholt, John P.

    2016-08-01

    We used density functional theory (DFT) to examine the partitioning of ferrous iron between periclase and bridgmanite under lower mantle conditions. To study the effects of the three major variables - pressure, temperature and concentration - these have been varied from 0 to 150 GPa, from 1000 to 4000 K and from 0 to 100% total iron content. We find that increasing temperature increases KD, increasing iron concentration decreases KD, while pressure can both increase and decrease KD. We find that KD decreases slowly from about 0.32 to 0.06 with depth under lower mantle conditions. We also find that KD increases sharply to 0.15 in the very lowermost mantle due to the strong temperature increases near the CMB. Spin transitions have a large effect on the activity of ferropericlase which causes KD to vary with pressure in a peak-like fashion. Despite the apparently large changes in KD through the mantle, this actually results in relatively small changes in total iron content in the two phases, with XFefp ranging from about 0.20 to 0.35, before decreasing again to about 0.28 at the CMB, and XFebd has a pretty constant value of about 0.04-0.07 throughout the lower mantle. For the very high Fe concentrations suggested for ULVZs, Fe partitions very strongly into ferropericlase.

  17. Inversion of hematocrit partition at microfluidic bifurcations

    CERN Document Server

    Shen, Zaiyi; Kaoui, Badr; Polack, Benoît; Harting, Jens; Misbah, Chaouqi; Podgorski, Thomas

    2016-01-01

    Partitioning of red blood cells (RBCs) at the level of bifurcations in the microcirculatory system affects many physiological functions yet it remains poorly understood. We address this problem by using T-shaped microfluidic bifurcations as a model. Our computer simulations and in vitro experiments reveal that the hematocrit ($\\phi_0$) partition depends strongly on RBC deformability, as long as $\\phi_0 <20$% (within the normal range in microcirculation), and can even lead to complete deprivation of RBCs in a child branch. Furthermore, we discover a deviation from the Zweifach-Fung effect which states that the child branch with lower flow rate recruits less RBCs than the higher flow rate child branch. At small enough $\\phi_0$, we get the inverse scenario, and the hematocrit in the lower flow rate child branch is even higher than in the parent vessel. We explain this result by an intricate up-stream RBC organization and we highlight the extreme dependence of RBC transport on geometrical and cell mechanical p...

  18. Non-Linear Canonical Transformations in Classical and Quantum Mechanics

    CERN Document Server

    Brodlie, A

    2004-01-01

    $p$-Mechanics is a consistent physical theory which describes both classical and quantum mechanics simultaneously through the representation theory of the Heisenberg group. In this paper we describe how non-linear canonical transformations affect $p$-mechanical observables and states. Using this we show how canonical transformations change a quantum mechanical system. We seek an operator on the set of $p$-mechanical observables which corresponds to the classical canonical transformation. In order to do this we derive a set of integral equations which when solved will give us the coherent state expansion of this operator. The motivation for these integral equations comes from the work of Moshinsky and a variety of collaborators. We consider a number of examples and discuss the use of these equations for non-bijective transformations.

  19. Canonical Entropy and Phase Transition of Rotating Black Hole

    Institute of Scientific and Technical Information of China (English)

    ZHAO Ren; WU Yue-Qin; ZHANG Li-Chun

    2008-01-01

    Recently, the Hawking radiation of a black hole has been studied using the tunnel effect method. The radiation spectrum of a black hole is derived. By discussing the correction to spectrum of the rotating black hole, we obtain the canonical entropy. The derived canonical entropy is equal to the sum of Bekenstein-Hawking entropy and correction term. The correction term near the critical point is different from the one near others. This difference plays an important role in studying the phase transition of the black hole. The black hole thermal capacity diverges at the critical point. However, the canonical entropy is not a complex number at this point. Thus we think that the phase transition created by this critical point is the second order phase transition. The discussed black hole is a five-dimensional Kerr-AdS black hole. We provide a basis for discussing thermodynamic properties of a higher-dimensional rotating black hole.

  20. Variation principle of piezothermoelastic bodies, canonical equation and homogeneous equation

    Institute of Scientific and Technical Information of China (English)

    LIU Yan-hong; ZHANG Hui-ming

    2007-01-01

    Combining the symplectic variations theory, the homogeneous control equation and isoparametric element homogeneous formulations for piezothermoelastic hybrid laminates problems were deduced. Firstly, based on the generalized Hamilton variation principle, the non-homogeneous Hamilton canonical equation for piezothermoelastic bodies was derived. Then the symplectic relationship of variations in the thermal equilibrium formulations and gradient equations was considered, and the non-homogeneous canonical equation was transformed to homogeneous control equation for solving independently the coupling problem of piezothermoelastic bodies by the incensement of dimensions of the canonical equation. For the convenience of deriving Hamilton isoparametric element formulations with four nodes, one can consider the temperature gradient equation as constitutive relation and reconstruct new variation principle. The homogeneous equation simplifies greatly the solution programs which are often performed to solve nonhomogeneous equation and second order differential equation on the thermal equilibrium and gradient relationship.